A Coyote is a predator and kills for a LIVING and it's survival. One of the favorite foods for the Coyote is domesticated dogs and cats. Do not let your dog chase them as he may think it's play, but the Coyote will know it's dinner. I would not try and poison them as your dog may get into it.
I really don't think you taking your dog in the woods looking for them is such a great idea as your dog may just venture out on his own never to come back. With coyotes in the area I would say you have a little hunting to do.