Your cousin didn't hit the coyote with the full load or it would've anchored it on the spot. You should be able to kill a coyote even out to 25 yards on a broadside shot, with bird shot, and kill it on the spot, but you need to hit it square with the full load. There have been many a coyote shot by pheasant hunters with bird shot!!
Maybe the politicians in your state are tree huggers and figure that they'll save all the poor little coyotes by making you use less than adequate means to effectively kill them at any distance, or maybe it's just that they like the idea of lots of wounded animals left to die a slow death[:'(]