Colorado is pretty liberal in dealing with coyotes. If one is damaging your property you can shoot it without a hunting license, and there is open season year round on coyotes for small game license holders. To use a leg-hold trap a special permit is required, otherwise it is illegal to use the trap. It is also illegal to feed coyotes or foxes, as it will make them want to hang out in residential areas and become a nuisance or aggressive towards humans.
If you see a coyote you want to instill fear of humans; yell, make loud noises, squirt it with a garden hose, whatever you can to scare it away, and not make it want to return. Coyotes diet consists 70% on smaller animals, mice, rabbits, etc, but anything smaller than the coyote is prey. Coyotes don't distinguish between a domestic cat and a wild rabbit, prey is prey. From PostIndependent.com.