RE: Is the 22mag idea for coyotes?
nope. the 22 mag will work okey at best. keep shots under 50 yards and try for a neck shot. if you want to get serious about yote hunting look into something like a 223, 22-250 and such rounds.
do you have any other guns? even if they are a 270 or above. i would take that over the 22 mag. you didn't say if you were saving fur? if you are use premium bullets through the larger calibers and it won't put a very big hole in them because there isn't evough resistance to open them up
good luck