If I were to start fresh now (or replace what I have) I'd get a savage with the accu trigger in 223. Then I'd top it with a Bushnell Elite 3200 3-9x40. Get a couple of good shooting sticks, maybe a harris L or BR bipod for prone/hood shooting, and the coyotes will be in serious trouble.
If you have you heart set on an AR then by all means get an AR. Just more expensive than the Savage. I hunt coyotes with both a bolt, semi, pump, and single shot and they all work. The semi is nice, but I can't remember a situation where I couldn't wrap the bolt fast enough for a finishing shot. But I've had three occasions now in the last year where I pulled the trigger, missed, and the coyote looked at me. On two occasion I moved to reload, cycle the bolt, and he made tracks. On the third occasion it was with a semi and I just pulled the trigger again.
But those situations are far and few between. I'd rather have the better savage with accutrigger and a few bills in my pocket verses quicker (instant) followup shots. But that's just me.
later,
scruffy