I always preface what I'm about to say with "if you want to shoot or trap coyotes, have at it", but killing coyotes doesn't have the positive impact on the local population of pheasants as one might think. If anything, coyotes are beneficial to the pheasants as they prey upon nest raiders like coons, skunks and possums. I won't argue that coyotes eat some pheasants, but in the grand scheme of things, coyotes and pheasants coexist quite nicely.