The coyote is a "non-trophy" predator. Predators are difficult to management because, as we all know, hunting and trapping are the most valuable tools fish and game uses to control wildlife populations.
The bottom line is, what value do they have. What we have created is our own problem. We now are at a point were wildlife, predators included, are not managed just for hunters, fishermen and trappers anymore - need I explain?
I agree with Jack, that "back in the day" coyotes wouldn't have been a problem and I'll leave it at that. Our snotty-nosed spoiled society turns to Government for everything - including toilet paper.
Perhaps Jack's, ideas are best as right now there are not many "legal" IFW approved methods to deal with an over abundance of yotes.
BTW, many people refuse to believe that predators kill just for the sport.