To the OP, I prefer a .243 with a 70-85 gr pill. If it is a dedicated coyote blaster, 22-250 with 40-55 gr v-max or nbts. If you practice a lot and don't reload, a .223 might be the best option because of ammo costs.

I personally have all 3. savage 243, vanguard 22-250 and ar-15 in 223. My favorite is the .243, because most of my coyote kills are during deer season and the .243 plays double duty very well. But a 20" or 24" barrel on an ar platform in .223 or .204 with good optics might be nice too.