Every quest has the possibility of awarding crowns, but certain event quests increase the chance of receiving one for its target monsters... or even guarantee it.

If I'm missing some, I'd appreciate if you drop a comment with the quest so I can add it. :)
(because i very well might be missing some here)

• A Rush of Blood - Odogaron mini crown
  
• The Greatest Jagras - Great Jagras gold crown and Devhiljo mini crown
  
• USJ: Gold Star Treatment - Great Jagras gold and mini crown
  
• USJ: Blazing Azure Stars! - Dodogama gold crown and Azure Rathalos mini Crown
  
• Egg Lovers United - Kulu-Ya-Ku gold crown
  
• Down the Dark Muddy Path - Barroth gold crown
  
• The Name's Lavasioth! - Lavasioth gold crown
  
• The Blazing Sun (Special Assignment quest) - Teostra gold crown

• Seeing is Believing - Tigrex gold crown
  
• Don't Forget The Earplugs! - Yian Garuga mini crown
  
• Paolumu Lullabies - Nightshade Paolumu mini crown
  
• Monkey Business - Furious Rajang mini crown

• Deep Green Blues - Anjanath, Great Jagras, Pukei-Pukei, Rathalos, and Tobi-Kadachi
  
• Wildspire Bolero - Diablos, Barroth, Jyuratodus, Kulu-Ya-Ku, and Rathian
  
• Coral Waltz - Legiana, Paolumu, Pink Rathian, and Tzitzi-Ya-Ku
  
• Effluvial Opera - Bazelgeuse, Great Girros, Odogaron, and Radobaan
  
• Rock N’ Roll Recess - Azure Rathalos, Dodogama, Lavasioth, and Uragaan

• Yodeling in the Forest - Anjanath, Rathalos, Nargacuga, Yian Garuga, and Rajang
  
• Heavy Metal in the Waste - Jyuratodus, Nightshade Paolumu, Glavenus, Black Diablos, and Savage Deviljho
  
• Symphony of the Coral - Paolumu, Legiana, Coral Pukei-Pukei, Ebony Odogaron, and Zinogre
  
• Rotten Canzone - Great Girros, Odogaron, Tigrex, Fulgur Anjanath, and Acidic Glavenus
  
• Alt Rock Recess - Banbaro, Uragaan, Brachydios, Azure Rathalos, and Seething Bazelgeuse
  
• Ballad of the Hoarfrost - Beotodus, Viper Tobi-Kadachi, Barioth, Shrieking Legiana, and Stygian Zinogre
  
• Muscle Monkey Madness - Rajang

Just as a side note so no-one will end up stressing over getting crowns for these guys:

Zorah Magdaros, Xeno'jiva, Behemoth, Leshen, Ancient Leshen, Shara Ishvalda, Kulve Taroth, Raging Brachydios, Safi'jiva, Alatreon.