Rabbit and Coyote
When rabbit and coyote are mentioned together, Tony Hillerman is most likely referring to a Navajo reference in which Coyote chases Rabbit, yet Rabbit gets the best of him.
In Navajo mythology, Coyote is a trickster or troublemaker. He is often referred to as First Angry or First Scolder and is said to have brought witchcraft into the world. He appears in many stories both as a trickster who cannot be trusted and as a sexual being who tricks others in order to get his way. He is a main character of the Navajo creation story.
In this particular tale, Coyote finds Rabbit and begins to chase him, but Rabbit hides in a hole in the ground. Coyote threatens to smoke Rabbit out using weeds. Rabbit replies, saying that he will eat the weeds before Coyote lights them on fire. Coyote says he will use pinyon pine, which is know for being a pitchy wood that burns hot and produces a lot of smoke. Using pinyon pine instead of weeds to smoke out Rabbit will kill him, showing the darker side of Coyote's trickster nature. But as Coyote puts his plan in motion, drawing closer to his smoldering pile of pinyon to blow on it and make it bigger, Rabbit kicks him in the face, escaping with laughter. Coyote lives to tell the tale, but his singed coat reminds us of how Rabbit got away.