I've had nothing but success on coyotes and especially foxes with my sportster .17 HMR. Took 4 coyotes last year from 35 to 153 yards - all one shot kills. 6 fox, 15 feet to 50 yards - one shot each too. My favorite fox caliber - no damage to pelts whatsoever.
Granted there are better calibers for knocking down a big coyote, but with good shot placement (all mine but one were broadside) the little .17 will do the job.
Love the accuracy of my sportster too!
Good shooting,
Mike