If a wounded coyote gets down a hole on ya, go find a piece of barbed wire. Usually a piece just a few feet long will suffice. Bend the end of the wire back onto itself and wrap it a few times making a small tight loop on the end. Now push the wire down into the hole. If the hole has a bend to it, simply turn/spin the wire as you push to feed it on into the hole. Once it reaches the coyote, or any furbearer, continue to turn the wire until it won't turn any more indicating that it is probably wrapped up into the critters fur. Now, simply pull the critter out of the hole. If the critter still has life, you may have a tug of war for a bit. If the critter is dead, it'll slide right out of the hole.
We had to use this trick this weekend to retrieve a coyote that a friend of mine shot. I've used it a few times over the years.