We have coyotes here as well.. they are starting to eat people cats and small dogs..
The aforementioned gut pile, dead cow etc.. Or a game call and BRIGHT lights works as well.. call them in, when they get near the target area, flip on the BRIGHT lights, and they will typically freeze for a few moments.. if your ready, and good, you can get them before they run.
A nice Mini 14 or AR works here, and I have seen shotguns with buckshot employed often... I like the mini over the bolt gun.. I could NEVER miss a running coyote 9 times with a bolt gun!