I thought about poison but too likely a dog might get into it. Live traps are next best bet then they can be taken somewhere and shot safely. For bears the live traps are quite large so not so easy. Mind you not so worried about the bears. They run from even if small dogs. I am more concerned in the event where you need immediate access such as an attack. The Coyotes will come right up to the house but lucky the dogs have not been around or inside. They are crafty buggers so you pretty much need to be ready right then if you want to shoot them. Might just have to hunt them. We live right next to town and I know they have killed a few pets to date.
I suspect many with real wild animal issues do not lock their guns away although they may tell people they do. Curious how many people don’t.