I'm astonished by hogdog. He vehemently claims that it is illegal to shoot trespassing dogs, it is not. He makes reference to making a trap out of a 12 gauge shotgun which is a second degree felony in Florida, you can get life in prison for making or possessing. Some people make it up as they go, hogdog is one and he ain't very good at it. My guess is he lets his dogs run the neighborhood.
I have lost count of the dogs I have killed and I have gone to court once, the civil lawsuit was dismissed, I whacked two very expensive afghan hounds to earn that. I killed a dog as a Jacksonville Sheriff's officer watched. I have killed several dogs as the owners watched, dont' do this unless it is really necessary. I killed a champion AKC registered doberman worth thousands of dollars, the owner of the dog called the Sheriff's office, the Sheriff of Clay County himself, Jennings Muhree responded (he rode patrol one day a week), told the owner all he could do was sue me. He didn't sue me. Two days later I watch one of Sheriff Murhee's officers kill three dogs serving a warrant. No big deal.
You have to know the local law, both state, county and municipal ordinance as the case may be, and you might be sued which is rare. It can cost you some money which is rare.
Do what you need to do and keep your mouth shut.
You can chum up any feral dog with dog food, makes it easy.
223 will do the job just fine. I use a handgun or 22, a lot of times a 22 to the back of the head as they are in a live trap. If the dog has an owner, a 22 short will force the owner to pay a big vet bill, he may learn something. It's only illegal if you get caught.
By far the best way to deal with dogs is to trap them, turn them over to the local dog catcher, or not as the case may be. Most animal control agencies will loan you a trap.
Heart of the Earth Products makes good traps, I have a 48D, it gets used regularly.
http://www.animal-traps.com/animal-trap-folding-dog-tc.html
A couple of these are handy:
http://www.animal-traps.com/animal-trap-covers-dividers.html#dividers