I agree with the above, your 22 just looses too much energy as distance happens, so KILLING power on both are not made for longer range work on Coyotes IMO
and even the .357 isn't a real long range coyote caliber, due to well, it just isn;t as flat shooting , even if it has the added bullet weight and energy!
so, making head shots can be tricky pending distance and loads being used!
if you want tio make quick clean kills, limit your distance on shot being taken , pending what rifle your using,
that or step up and get your slf a new rifle with some more longer distance abilities!
even coyote's should be shot with humane intentions for fast clean kills, and not just shot at and wounded!