In Southern NH it is rimfire only. As Tango stated, the .17HMR is not a coyote round. I use a .22WMR w/ 40gr HP's, never the 30gr plastic tip variety. 75 yards would be max, unless a good headshot presented itself. The problem w/ that is I have yet to see one stop for more than a second or 2. Most folks here use a 12ga w/ #4 lead. Good to 40 yards w/ a full choke.
Now if you look at a box of .17HMR, the 20gr Gamepoints do have a picture of a howling coyote. It is a marketing picture, that is all. The 30gr .22WMR and .17HMR work very well on fox and woodchuck(P-dog).
Your .22lr will make for a fun day w/ P-dogs.