if you reload, go with the .204 and 35 gr. bergers on top, and if ya don't reload stick with the .223.
I've shot just short of 100 coyotes this past winter and most of them with a .204 and the 35 gr. berger. It just flat works well.
With that said, I've shot almost 20 with my .17 rem. and it works pretty well to.
If ya start getting a lot of run offs, move the bullet further forward and find the shoulder. Bullet placement is key to plant'em where they stood.