I didn't even hunt coyotes until a farmer asked me to. I shoot groundhogs on his land, and as soon as he told me about losing a sheep to one, I felt I owed him...so I did. I wasn't successful, but the coyote(s) never came back either. Maybe seeing my fat a** in the tree line with a .223 put them off. :)
Had this conversation recently online too ABOUT groundhogs, and whether or not you should wait until the young are weaned before shooting adults. From a hunting perspective, more targets=better. But, I personally find it a bit disingenuous to be granted permission to rid their property of these things and then pass on shot opportunities for the sake of my own "sport".