RE: big coyote problems
Traps, and lots of 'em. Contact your local ADC/animal damage control guy and have him trap'em. I good trapper will be more effective than the best hunter every day of the week and twice on Sunday.
If ya can't afford the ADC guy, at least ask him for advice on how to set traps because just putting traps out willy nilly won't cut it. And buying and setting them yourself may save you some money, but in the long run, having it done by a preofessional will be quicker and probably cheaper.