Having taken game with my Hummer's, I know that it can be done ethically and humanely... but as I said, that involves accepting the limitations. If a new coyote hunter was heading out looking for his first coyote, I would not recommend using a .17 HMR... why??? Because the temptation to lob bullets at a yote that hangs up at 300+ yards will be too great. A newbie would be better off with a standard centerfire caliber (.204, .22/250, .223, .220, .243 etc...) at least until they are experienced and can be mature enough to wait for a proper scenario for a humane kill with a lesser weapon.
P.S - this question was always going to draw heated opinions... it does every time it comes up.
To the OP~read this ^, Hoyt said it better than I did. I've been coyote hunting (have yet to shoot one) but didn't even attempt this until I had a .223. (had a .17HMR and a .22WMR in the safe at the time) ZERO temptation to shoot one with a rimfire. The fellow I hunt with has been at the coyote thing for years, also has an HMR, and has never once taken it out for coyotes. He started with a .223, and moved UP to a .243~both of which anchor a coyote very well. I haven't heard anyone say an HMR won't do it, but you'd have to be a little off-center to get yourself believing it's the best tool for the job. Don't think it's simply power-hungry hunters using centerfire rounds like .204, .223, .243, 22-250. These are proven varmint calibers that have more reach and power than and HMR by a long shot. So, don't go by my experience, look around...ask even more hunters...look online...see what hunters use for coyotes, .17HMR probably won't pop-up very often.