For killing coyotes when fur is not a consideration, any gun is fine.

I have killed coyotes with 22LR up to 50-140 Sharps and with pistols from 22 LR to 454 Casull. I also have killed a few with 40 and 50 cal flintlocks and one with an arrow.

When fur in prime and fur prices are up you want bullets that don't leave big holes in the hide.