"Verminators", is the best IMO. Host Rick Pallet which is from my hometown here in Kansas along with Randy Anderson, from Nebraska make the show. They shoot bobcats, coyotes, and foxes. Some of the spots on that video, look familiar, plus Rick is a goofy guy that is fun to watch.

The best for just coyotes is "Calling all Coyotes" 1 & 2, which is hosted by Randy Anderson from Nebraska.