I would not consider shooting any animal the size of a coyote with any rim fire. The exception would be finishing a trapped animal. Some western states are paying $50 dollars in bounty money. A centerfire rifle can soon pay for its self.
If you're in situations where you aren't dealing with shooting through brush and you can take a good rest and shoot the coyote in the head and you are confident in doing so then the 17 is plenty good in my opinion, 50 yards isn't too far, I have seen coyote killed with 22 mag and 22 lr at that range as well with good shots, however being that your ranges will often vary as well as ease of shot placement I prefer a 223 or 22-250 for coyote or a 12 guage and 4 buck.