Are you recovering these for pelts? Are they a nuisance animal in your area?
Here, they are. I don't fur hunt, and ours are mangy disease spreading nasties. So, in protecting the farm critters from them, and thinning as many out as possible (we have many red tails, martins, fox, and bob cat to thin the local vermin) I just shoot them. Where I hit them isn't important, normally head/chest, but I personally do not sweat the placement. Let God sort them out.
You'll have to excuse my disdain for coy dogs. They're thick here, and cause problems quite frequently.