Like Tracker 721 my goto coyote hunting rifle is a 222 Rem, but most of my coyotes are called so ranges are usually under 200 yards and most are und 100. I do have a 22-204 that is my open country pelt hunting gun. I have a nice little custom Rem 722 in 22-250 that I use for control work when pelts are worthless. Pelt hunting I can pass on a marginal shot, when doing control work every coyote needs to drop.
I won an AR in 20 Practical and will give it a try this coming fall but I'm not a big fan of the platform for predator hunting. The 5.6x50R Mag and 5.6x52R(22 Sav. Highpower) have worked well on coyotes in my combo guns that I run when hunting the really thick stuff.