Start the game. Pick endless night. Select friends only. Enter the game. Select the Swat guy. Press [Esc] to pause the game. Open Steam overlay. Send invite to a friend via Steam overlay. Close the overlay. Keep the in-game pause on.

As soon as your friend joins he/she will be unable to play with you. He/she will be in your lobby, but not in your instance.
His/her clock will be ticking, he/she will not spawn, and all he/she has to do is wait for 5 minutes.

Tell him/her to return the favour.

Once it is your turn wait for his/her invitation via Steam overlay. Join the game. Select the Swat guy. You won't spawn, but the clock will be ticking. Wait for 5 minutes. Profit.

I hope this helps. It has worked for my co-op partner and me.

Might work 100% if the ping is high.