I can only tell you what I've read and most say even the heavier .22 magnum is too weak. I watched 17 HRM blow up prairie dogs and I've no doubt it could kill coyote but...
If your thinking about buying a new rifle what about a NEF single shot in .22 Hornet? They're cheap, certainly accurate enough for 100 yards and a hornet makes less noise than a .223 would. (GO has a seperate forum for NEF fanatics which you may want to visit for more info)
I will admit I have taken my .22 mag out on rare occasion with the intention of popping a coyote but I fully understood I was most likely under gunned and needed a lung shot.
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Even this small red fox went farther than I ever thought he could with a 25-06 hit. He was hit a tad too far back.