I've seen a pack of coyotes gang up on a dog- big pit bull mix- and basically try to tag team him down. He grabbed one, two others would grab his back legs and make him turn loose. Meanwhile the others would be resting up to swap off when the fighters got tired, never giving him a chance to rest. They ran at the first shotgun blast, but if we hadn't been there that dog was a goner.
As far as the original question, I don't believe that shooting out nuisance animals of any kind is more than a temporary solution at best. You have to find what's attracting them into your area and change that. Coyotes are spreading across North America, so that might be easier said than done. Mostly they replace wolves, which have been eradicated in most of the USA. Do you still get them in Ontario?