The .17 HMR will kill a coyote, BUT it won't "bang flop" a coyote, so unless you're darn good at tracking, I wouldn't recomend it. Don't expect any blood trail, because there won't be enough to track, because most likely there will be .17 cal. hole in and no hole out. I often wonder when we hear about the "great success" on coyotes with the .17 HMR, how many of the lost critters go untold!
For everyone hunter touting it's great ability, there are 3 others saying that they tried it and learned the hard way with lost coyotes! I've shot 100's of prairie dogs with my 17 HMR, and just from that, I don't see it being the right choice for coyotes!