surprised nobody has mentioned 6mm arc yet.
I dont hunt coyotes, but have a lot of friends that do. I am an AR guy though and I was fascinated by 6mm arc's potential as a gas gun long range setup, to give my 6.5 creedmoor barrel some extra shelf life.
6mm arc gets the upper hand if you already own a smallframe ar (unlike 6.5) because you can just build yourself a 6mm arc upper and slap it onto your existing lower. You will need a new bolt (6.5 grendel bolt) for it, but the charging handle and carrier can be reused from your existing ar as well.
I built one for about $1,500, using a 18" SS Proof barrel as the base. It was very easy to ring steel with it at 500-600. Boringly accurate. The 80 grain hornadys seem to be the goto for coyote disposal. At 100 it groups sub-moa on 10 shot groups as well.
The benefit is, you can do the same with a 14.5" or a 12" arc barrel, from what I hear. Im considering building a shorter one for that same reason, and as long as you dont bolt a bunch of nonsense onto an AR, they can be reasonably light too.