Snakeman, I've never even had a coyote in my sights, so you may be asking the wrong guy. All I can tell you is, the Mini-14 is not generally as inaccurate as some have painted it, and recent production Mini-14s are more accurate than they used to be.
Alternatives? Compare a new Mini to a good, used AR and see just where the budget is right now.
If coyotes and feral dogs need to be eradicated right now, nailing a bunch of them with a Mini that can be in your truck today or tomorrow beats heck out of letting them kill livestock for several months until the AR15 budget has been met, even if you have to pass up some of the longer shots. You can always trade in the Mini on an AR later.
FWIW, the Ruger Mini-14 has been my patrol car rifle since 1993, and I've never felt a need to replace it with one of my AR15s.
I'd suggest posting your question on the several other GATE forums that cover AR15, long range shooting, etc. for different opinions.
Let us know what you decide on!