Bruce
Herd Master
I know that one, and actually likely begot the bigger problem ... DD1. The emotional vegetarian who thinks that animals have to live their lives too. Yeah well, I don't think domestic chickens in a fenced area is the natural food of coons and foxes. I scared up bunches of voles when I was out mowing.I'm not super happy about the no gun road block, but I married him.
But to keep peace I don't have a gunpowder gun. And they don't know about the pellet rifle in the barn. At least I've not had your problem of a "too friendly" coyote. I suspect if I did I'd be saying "tough noogies, I'm not getting attacked by a coyote for your belief system".
Good luck. BTW, don't know about there but WallyWorld doesn't carry anything but pellet and BB guns here. I'd go to a gun/hunting store where they know their inventory and can tell you what the best option is for you and your specific situation and quarry. They might also know where you can get training if they don't have that themselves.