.22 mag would work good or even .222 swift if you did not want to go to .223
Must be a typo since there is no such thing as a .222 swift. There is the .222 rem. and the .220 swift, but no such thing as a .222 swift.
If ya shoot'em with a .22lr, don't come back here telling us about the coyote/s that got away. There will be no blood trail, and anything other than a spine shot or brain shot, the coyote will run like the wind, as if you never even hit it and you won't recover it.