Thanks to all for comments and suggestions.
Some years ago, I had a visit from a bobcat (I had goats at the time) but had no problems. I had called to make sure it was okay to take the bobcat out if it was a threat but it wasn't and, to be honest, it was a beautiful animal.
Every now and then, we get a stray dog or two on the property but those are usually easily sent off. Never any coyotes.
I've seen foxes nearby but none has ever come on my property.
Animals seem to sense that coming onto my property is a dead end and avoid it for that reason.
I hadn't really thought about range but we do have neighbors across the water (some canals so not that far away) and sometimes obscured by trees and brush along the water.
Range to these varmints would be no more than 50-60 feet. So, a .410 would be effective at that range and present a minimal down range risk?
Also, regarding a .410 -- would that be a gun my girl friend would be comfortable in using. I've got a 12 gauge Mossberg and I know that kickback would.
I've not had good luck with traps in the past but they may be worth a try.
I spent 4 years trapping, removing and killing nuisance wildlife as part of a commercial pest control company. We trapped and killed Coyotes, raccoons, armadillos, wild hog, opossums, turkeys, birds, feral cats and snakes that found their way around the commercial buildings we serviced.
So here's a few things I learned. The first couple of things are that you will not catch coyote or bobcats in a live trap without using live bait, a bunny rabbit works best. The second thing is if you trap an animal forget about relocating and releasing it unless you're willing to drive at least 25 miles or so and risk getting caught releasing it. A lot of times cats and raccoons will find their way back. We tested this by spray painting both raccoons and cats when releasing them sometimes 10 or more miles from where we captured them. Once trapped and then released they are next to impossible to trap or get close enough to shot a second time. I would avoid trying to shoot at them unless you are a good shot and at a close distance. If you miss they become very cautious but may not leave.....In other words they become better pest....Save your ammo until the last step as I'll explain later.
Your best bet is to try trapping them first. Leave your traps outside to help eliminate human odor, under trees and in the dirt are great places. Once deciding what you're trying to trap you'll be able to determine the size trap to use and what bait to use. Look for "paths" where animals have been walking as they will tend to use a route when foraging. Place the traps close to the path. Use multiple traps as sometimes curious animals will spring a trap while investigating it or figuring out how to get in.
Once trapped be very careful if you have to move the trap, most have handles on the top. I always used heavy gloves and sometimes a hook to lift the trap. Feral cats and raccoons can stick their arms through the openings and have laser sharp claws. Now to the final step....If your trap and animal are in an out of the way place where you can't be seen by anyone, you're golden, if not then move it to such a spot. Now comes the fun part....Take the firearm of choice and tap or poke at the trap with it which will usually make the trapped animal jump at the barrel and blow the little bastards head off.....then discreetly dispose of the body. Job done.