If you aren't opposed to the larger frame of the AR10 style rifles, go for it. I don't feel its needed for coyotes as there are a LOT of calibers for the AR15 that will do the same work.
The only reason IMO, to jump to the AR10 would be to run a .260 or a creedmoor, and both are WAY PLENTY OF GUN for coyotes.
I shoot a .243WSSM and with 105 gr bullets, it completely destroys them. My partner gets upset because he likes to save fur, and there usually isn't any worth keeping if I let a pill fly.
Depending on your shooting distance, there is no reason to look beyond the 243 or 25 WSSM if "larger than .223" is what you're after.
If you don't plan to shoot beyond 3-400...then a 6.8 might work better...but the point is. AR10 isn't really necessary. LOTS of calibers in an AR15 will wreck a dog.
Maybe consider the 22-250. Not bigger, per say, but plenty fast.