Re: .22 MAG too small for coyotes???
Coyotes are tough customers and I do NOT recommend using anything in rimfire.
You mentioned having a pest problem. If they're being removed from the planet, then there's no such thing as overkill. Dead is dead.
After too many runners, I stepped up to a .25-06 and have yet to get anything other than DRT. If you talk to professional coyote hunters, they all use larger calibers to put them down...on the spot.
If God didn't want man to eat animals, he wouldn't have made them out of meat.