I killed a coyote earlier this week (having trouble getting the pictures to embed) that succumbed to a 20 gr V Max from my 17 Rem. Not the optimum bullet, in my limited experience. The 17 or 22 rimfires are about the minimum for coyote-sized varmints, but there is a lot of room between the 17 HMR and the 17 Rem, and lots of good bullets. You should be able to find something you really like. A 17 Hornady Hornet will be my next toy and I expect it will do a good job on coyotes and a better one on prairie dogs.
The hide hunters often mention that the light bullets tend to leave only an entrance hole. I can verify that.
