I run all AR's for coyotes. Custom built on bushmaster receivers, I have a rebarreled and tweaked Varminter 24" heavy barrel and a 16.5" custom Hbar. Both in .223/5.56. Sure, a heavier caliber will anchor them more reliably if you're not a very good shot, but the .223 is plenty for as far as anyone typically will hunt dogs (500+/-). I put up fur, so I'd rather keep my dogs in one piece.