I would think that you could get a decent used 222 or bigger for about the same price as a good .17 or .22 mag. That's what i would do if coyotes were my priority.

As for comparing the .17 vs. the .22 mag, I've knocked a crow out of the top of an oak tree at 240 yards with my .17. Dunno how many folks can say the same thing for their .22mag.