Coyotes have been absolute hell on small game and farm animals in the area where i own land in Illinois. A few years ago, two different groups of coyote hunters started hunting the area regularly. Now the coyotes are much less of a problem.
I have to agree with Lance, as long as it is legal then by all means go for it. Coyotes here are a problem too. This past year for once the coyote numbers were down. So yes as far as I am concerned keep on getting those numbers under control.