ORIGINAL: James B
The 22-250 would sure get my vote for all around varmits including Yote size varmits. The 243 will do the job very well also but I prefer the 22-250. Less noise and recoil. Very accurate and shooter friendly. Out to 300 yards, the 223 will do the job cheaper than anything and nearly as well.
I'll second that. I hunt coyotes a lot, and have never felt undergunned with a .223. I also have never had any trouble with bullets exiting and messing up the hides. Shoot something smaller than a coyote, and you may really see a difference. A .222 isn't bad, either.