Some methods I discovered on the internet, so if I'll manage to find the material again, I'll credit them there for sure.

Some of the methods I've come up with may not be optimal for you, but they worked for me as part of research in that regard. If you find you way to optimize them, do it.

Some methods will require you to be offline in-game. You can do that either by going offline on steam or setting up a firewall rule of blocking connection to DSII.

Farming may be a tedious process. Don't push yourself to farm from start to finish, because it's not fun to do so as RNG likes to put some fingers up your butthole. Take a break, put some background like music or video to make it less of a chore. Putting music on the background and videos in between farming certain covenants helped me immensely.

Starting equipment can really decide the way how you want to get 3rd rank on some covenants - quick or long way. So if you want to get rid of 2 covenants in the early game, take bonfire ascetic as your starting gift.




While you will be on your adventure, consider grabbing these on your way:

This should be your very first covenant to join during an adventure. And it's easy to farm because the requirements aren't that big. This covenant supposes to be helping you against invaders - Blue Sentinel members who wear a ring and when you also wear a ring from the way of blue, you have a chance to have an aid of blue phantom, that must destroy the invader. Well, but we can't have them online. So in order to level this one, you have to kill invaders OFFLINE. The reward table is:



So, not many kills. If you will be only at this covenant, it's easy to get 3rd rank by just playing. But we are here to get it in the fastest way.

So, there's a special offline invasion that happens at the Grave of Saints. The invader's name is Rhoy The Explorer. He spawns once at bonfire intensity 1, but remember you got bonfire ascetic as starting gift? Well, this is the reason why I pick it.

So you have to kill the boss of this area first. After killing, you need to burn bonfire ascetic at HARVAL'S RESTING PLACE bonfire. If you burn it in 2nd bonfire, right before the boss, you'll get only boss spawn.

When you burn it there, Rhoy will spawn 12 times. Well, you have to kill him 10, with a slight minus, times (if you killed someone already). And that's it. You can dispose of him by any means necessary because he is not really a threat compared to the Company of Champions covenant.

If the game is not hard enough for you, then you are the champion! This covenant is one of the first available covenants at Majula stone behind the way to Heide Tower. When you are a member of it, the game has increased difficulty (take more damage, inflict less, no summons, etc.), but also you can get a small benefit of item discovery boost (by unknown amount). In order to gain rewards, you earn Awestones, which can be dropped by certain enemies or by killing invaders.

The table of rewards:



These are quite good rewards. 2nd and 3rd rank gives you rings, that increase stats and give massive damage to bare fists and the ability to power stance fists. I usually like to play this way, so apart from getting 300k+ souls, you also gain a good "weapon".

So, I used to farm it right away, as opportunity meets the requirements, but I've realized that you may want to hold on to it until you will get all needed item discovery increase items. Why? Because in this area, there's also one more covenant to farm - Rat King. But you want to join it after you get the 35 rat tails (more on that later).

Anyway, we discussed that there is an offline invader, Rhoy. Well, at bonfire intensity 2 and being a member of CoC, he spawns an infinite amount of times. Well, this one is a bit tedious, but I think it will be a worthwhile investment.

Here, I will explain the easiest method (without rat king farm, more on that in Rat King section) on a self-drawn map:



This is the 2nd floor of Grave of Saints. Make sure that on the 2nd floor the bridge is lowered. Go down where the ladder is and climb back up. This triggers invader spawn. Pass the bridge and try to stagger Rhoy with either Force miracle or something that does good poise damage so that he will be stunlocked. Direct him towards fall, so he dies. No worries - you'll get your awestone instead of the human effigy. He has a very small chance to drop an extra awestone, but it is so risky to tackle him in CoC, because he inflicts a big chunk of damage, if you are poor on Vigor.

After you receive awestone, go back to the bonfire and proceed to do that 49 more times (put something on the background to amuse you). Don't forget from time to time spend your souls on all your needs.

Jerma reference inside your Dark Souls game? Count me in!

This covenant is for those, who like to intercept tresspassers. In 2 areas (Grave of Saints & Doors of Pharros), wear a ring and you can invade someones world to kill them. The reward is rat tail and, IIRC, Pharos' Lockstone. The table of rewards as follows:


Honestly, I've never seen an invader on Rat King's behalf. It's kinda not popular due to rewards being really mediocre. Well honestly, silky stones sometimes can be useful, but only RNG will decide what you will get from them. The slumbering ring is not that useful due to the lack of invisible body spell (from ds1 & ds3). What I suggest to do is to visit it from time to time in order not to get bored. Or you can combine it with CoC and you can farm 2 covenants at the same time.

Let's refer to drawn maps again. Let's start from the first floor:





Once you get all gear for item discovery, start from Harval's resting place. Takedown 4 rats at the entryway [1] and proceed to the 1st floor corridor [2]. There will be 3 rats - deal with them. If you have Pharros' Lockstones to spare, you can lower the bridge to get through the area with 3 more rats [3]. But you can always climb up the ladder. That leads us to the 2nd floor:




You might want to trigger some rats, that fall out of the ceiling holes by running a bit below them. Then proceed to lure the last 3 rats in the corner [4]. While you wait on ceiling rats to come down, you can take out these 3, then proceed on destroying whatever rest decided to come down and eat your flesh.

Oh, forgot to mention, that those rats spawn infinitely, doesn't matter if you are in CoC or not, but don't join Rat King's covenant. That will trigger the benefit of it - enemies of the area won't hit you, but neither you can inflict harm on them. Like I said before, get 35 tails and then join to turn them in.

*Flashbacks of cheaters & twinks intensifies*

So this is the covenant, where you can get really rich with titanite chunks if you defeat the host. The purpose is that bell keepers... well... keeping the bell from trespassers. Whenever you wear a ring you've been given by a mad dude you talked to, you can be summoned in the Belfry Luna & Belfry Sol to stop the host of the world. The rewards for ranks are:


If you are looking to complete achievements, this is essential to get 2nd rank due to achievement, where you get all sorceries. There is NO way around it. You have to get 2nd rank to get one of the most useless spells offline. If you are mad enough to grab some fashion, you can get 100 kills.

But we aren't playing online. So how are we gonna do it? Well, while offline, in Belfry Sol, there is a chance that you will see this guy:




This is The Mad Warrior. And it's an easy opponent as well, so the goal of 3rd rank is to kill him 100 times. You can do it the normal way - climb up, kill all enemies, search for him near the bell, go back to the bonfire, sit in it, and repeat. Quite a long way to get him.

But what if I told you, that there is another method. It's relatively long enough as well, but it makes part with going up and down less tedious. I think there's no need for an explanation on how to because I've got this from this video:


But in case of this video will be gone, here's an explanation:
From 2nd bonfire of Iron Keep, head out and kill the dude that straight of you. Now proceed to place with 2 Alonne soldiers + Turtle - kill them. Now you have to clear the whole room with an elevator platform (except 2 Alonne knights, where you have Oliver invader - they are gonna be needed). Next, head to the Belfry Sol, and kill every last bugger you see. And you need to do that until ALL enemies will be eliminated (despawned).

After that, make sure that everyone is dead. Good? Now get a miracle by the name of Unveil and any chime you can wield.

Sit in Belfry Sol's bonfire. Cast it. You need to wait a bit and see if that glowing eye will head towards the metal grate you see. if it goes far through it, then this will be an indication that mad warrior is here (if the video is still alive, you can also check examples of bad spawns).

So what I usually do is I am getting 5 kills normally and then progress accordingly in the game. Not tiresome and doable to achieve.

*But you don't stick to honour code* gang

So this covenant focusing on getting dragon scales in duels, that you can acquire in PvP combat. You put dragon sign, someone summons you. And if you win, you get a Dragon Scale. In order to join Covenant, you have to grab an egg in endgame location - Dragon Shrine. The rewards are:



But good for us is that the same location, where we snatched dragon egg, has also a lot of "Dragons". Yes, those Dragon-looking guards also drop Dragon scale as a chance. But tackling them can be challenging process. But fear not, there are some easy process to wipe not just 1 by 1, but groups of them! I couldn't be able to fit a whole map in both size and in A4 size, but this one has also a good video:


But, again, if this video will be unavailable, here's the text version:
So the plan is simple. If you have requirements to cast dark fog, then attune it. Otherwise, you can get poison mist and toxic mist and use pyromancy glove. Put every single gear increase. Bonus would be joining Covenant of Champinons, because it's not just gives you a chance, but also gives you ability to farm awestones, in case if you haven't completed Covenant of Champions.

So you have to first open 2 wooden doors, Now head back to the first 2 dragon guards and from now on, trigger them to attack you. The more you trigger, the better. But you also have to VERY fast to get to the door. Close the door from the other side. If 2 guards that very close to the door will simultaneously start opening it, the will be stuck in the sequence, where they try to correct themselves in the position of opening door. Now, you have to cast a spell of choice you picked and cast it right to the door. It will go through it. And if you see the enemy health start depleting, then you are golden. You have to do it couple of times though, So make sure that you will get either spell usage items for refill, or get enough attunement to get multiple spells (maybe even all 3 to fit).

Same thing from other side, but easy part there is that you need to trigger only one enemy - the rest will come. But you need to do that on top door this time. After you killed all of them, there should be lots of souls and potential dragon scale.

Keep in mind, I wasn't able to make door strat consistantly, so if there will be a case that it might not work, resort to the any possible way to dispatch them.

Engaging in jolly co-op? Nah, that's not for us.

So, one of the most famous covenants, that exist in all 3 games. The idea of covenant is to focus on helping the host. Upon fulfillment, you receive a medal, that you trade at the statue (which you can find in harvest valley). The rewards behind this covenant are:




Well, if you are looking at doing all achievements or having that miracle for FTH builds, then you can give this one a go. However, you may have to hold this one up until you get NG+ (cannot confirm in regard to bonfire aesthetic use).

So how we will do it? Again, you need to have a bonfire intensity 2 at the bonfire - Royal Camp Site. There are multiple falconers across that camp, that drop you sunlight medal. But it ain't big of a chance, so you have to put LITERALLY everything to boost your item increase. When you get your first visit, I suggest killing big boars the first time, because to farm this, you don't need to be a member of Heirs of the Sun. You need to be in Covenant of Champions!

You can tackle falconers in every way. But there's an easy way if you invest in 2 miracles - Soul appease and Promised Walk of Peace. The way how it works is simple:




Stand near a wall where the green point is marked. Cast Promised Walk of Peace. This way you will aggro enemies to you, when 3 falconers will be in close proximity, cast Soul Appease. Since falconer is an undead type of enemy, soul appease will deal damage to them. You might not gonna have enough to cast once, so near that green point, you can just circle around and cast another one. Then sit in the bonfire and repeat. I suggest as well to prepare a timer for 5 minutes if you use rusted coins. Once the effect will appear, start a timer, and once it's done (and you are still alive), reapply buff.

Also, the reason that I marked at least 2 falconers that can't be killed with the setup is that you aggro them, but they are going to snipe you with arrows. So be careful.

Video in action:

I know that it's not a covenant exactly, but it's also worth mentioning, due to how familiar it works to receive those awards. So this is an endgame location - Crown of Ivory King DLC. When you face the last boss of this DLC - Ivory King, before his appearance, you have to fight some charred Loyce k***ghts. They have a chance to drop Loyce Soul - an item, that doesn't give you any amount of souls, but they act somewhat like a Soul of a Giant. Each time you get a certain amount of Loyce souls, you can talk to Alsanna (the girl on top of the entryway to the boss area) to open little by little frozen ice, so you can talk to her and receive the final award. Oh, speaking of awards:




Quite hefty work you need to do here. And it's quite hard to find a window to attack enemies in there. And you have to refrain from using your armor of choice because this is the one where it's better to put every boost of item increase possible. Anyway, whenever Ivory King gates start to appear, you have 3 options:

1. Die by gravity
   
2. Use homeward bone or Feather
   
3. Use homeward miracle

You see, whenever you fight them pre-boss phase, you have assistance with your own cavalry of 4 Frog bois. When you kill the boss, you can still farm, but it will be significantly harder to pull that off. So, consider it before killing, if you determined to get them.

Well, that's all possible ways to acquire covenant items in the game without ONLINE involvement. I haven't mentioned the Brotherhood of Blood and Blue Sentinels, because there's no way you can get their ranks offline. But what's good is that FromSoftware introduced rewards that are scattered around Drangleic across multiple playthroughs. So I suggest referring to the wiki and finding specific items that are locked behind these covenants.

Big shotout to the channels that I used material to show it live and shortened my guides significantly. Also big thanks for wikidot of DS2 for pictures that used in this guide. Schemes were made in Microsoft Visio.

That's all. Happy hunting, folks!