Let's See...

Dog chase things that's what they do.
Coyotes chase things that's what they do.

You can't blame a dog for being a dog.
You can't blame a coyote for being a coyote.

Its not the dog's fault for a bad owner.
Its not the coyote's for for not having an owner.

Its inhumane to shoot a dog.
If its inhumane to shoot a 45# dog with highpower rifle is it inhumane to shoot a 150# deer with the same?

Shaner you did good by gettting the problem reported but if it persist do what you feel is right.