When I bought my Mini-14 I labeled it my coyote gun, I have yet to use it on a coyote. I still think it's about the perfect rifle for that purpose even though all the coyotes I've killed have been while deer hunting and I've used my deer rifle for them. That being said I don't live on a ranch where coyotes would be targets of opportunity, I would actually have to hunt them to use the Mini on one. I would absolutely go with a Mini as a dedicated ranch rifle. None of this is to say that a quality AR wouldn't do the job and in an M4 style rifle would probably do it very well, I just prefer the Mini to the AR. I've always been a wood and blued steel kind of guy, but I don't think you could go wrong either way.
Stu
Stu