Another vote for the .223. I load a 50 gr V-Max over 26.5 gr of Varget for 3200 fps. Three rounds generally go through a ragged hole at 100 yards from the CZ 527 Varmint Lam I prefer to carry for coyotes. Significantly less pelt damage than my .243 or .22-250 inflicts.
On windy days when I'm not concerned about pelt damage (i.e. late spring or summer), I prefer a .243. I haven't finished working up the load yet, but the 75 gr. V-Max over 45-ish of IMR 4350 is showing promise in the accuracy department through an older Ruger 1B.