I love and respect all kinds of life. For instance I think spiders are fascinating and clever but I don't want them in my house. The same can be said for many species and I wou want them in my backyard.
Aren't coyotes the tricksters in many american native stories? Be careful that he hasn't tricked you into thinking he's not around. Maybe give the dept of natural resorces a jingle anyway and see if they have any tricks for keeping the nonnative trickster out of the state.