Admittedly, I am not fur-centric on coyotes; I just kill'em.

Anything that'll kill'em, and which is legal in your jurisdiction (and that is cheap to feed, or that you enjoy shooting) is just the ticket.

.17 HMR will do.

So will an '06.

3 1/2 -inch 12 and 10 gauge turkey loads do the job, too.

My best hunting buddy swears by the .22 Mag.

Other dudes say the .22-250 is the way to go.

Like I say, anything that'll put the whack on'em and which is legal to employ for that purpose where you're at is the way to go.