AR,pump,lever,bolt?? I think the best coyote gun is the one you have when you see the D--- things.
I have several rifles I use for shooting coyotes depending on the situation.
I use an AR a lot when I'm calling, especially when my shots will be 200 yards or less and there's a good chance I'll call in mutiple yotes.
On mutiple targets I'm quicker with the AR then I am with a bolt gun.
When I'm calling from the edges of bean fields and there's a chance the shots may have to stretch to 350 yards I take my 22-250.
If I'm hunting and I think I'm going to have shots past 350 I take my bull barrel 243.
This rifle is a sweet shooter but it's not one I care to pack very far anymore.