Coyotes numbers have been expanding rapidly in Alabama for several years, but only recently started seeing them around here. This concerns me a good bit because we have 4 nieces/nephews, and our son, who plays in the yard. My wife and sister go out there a good bit as well. Also have a couple small dogs and some cats. I realize coyotes normally aren't aggressive to humans, but they are to animals, and if they are mixed coy-wolves/dogs they would be much more likely to not fear humans.

Roughly 2 months ago, I noticed a dead coyote pup on the side of the road about a mile from our house. The pup had a mostly grey back, muzzle, top half of neck, lower legs, and tail; it had black sides, feet, and throat; also had brown mixed in everywhere, but more prominent on its sides, throat, chest, upper legs, and hindquarters. Since then I've seen 5 or 6 more in varying states of existence, and while they all had similar coloring, I wasn't able to get a long enough look at any of them to be able to detail their markings.

Fast forward to now, I haven't seen any the past 2 weeks, but in the past 2 days activity has spiked WAY up. I still haven't seen any, but I sure can hear them. There is a pack somewhere nearby, and they are howling like crazy. I've heard them only twice today, but yesterday it sounded like they were having choir practice all dadgum day. Multiple high pitched calls, with 5 or 6 simultaneous, individual "voices". At times, it almost sounds like they are singing harmony together. It's a mix of yipping, minimal barking, and a lot of howls that occasionally sounds like screaming. When they let a long call loose, it's high pitched enough that it occasionally sounds like something whistling. Similar to what I've always heard people claim bigfoot sounds like.

We are in the Appalachian foothills, and have roughly 17 acres of open ground bordered by an old growth forest on 3 sides. There is a road on the 4th side, with 3 houses separated by large yards, and then more forest behind them. The calls are mostly coming from the woods behind our house, but they do move around a good bit.

The only guns we have are handguns, a .410, a 20 gauge, and 2 .22s. The .22s are not going to do much damage unless I get a heart or brain shot, but the cheap 4x scopes on them aren't accurate enough to allow that from 200-600 yards. And the shotguns/handguns aren't worth anything past 30-ish yards.

What gun should I look at? I have a bad shoulder and can't shoot any large caliber rifle, I've tried a few times and they are extremely painful. I am assuming most would say AR, but I can't really afford one at the moment, unless someone wants to be a pal and give me a deal on one. Would something like a youth .243 do the trick? They aren't horribly expensive.

Also, what should I know about trapping them? Is there a "Trapping Coyotes for Dummies" type of article or website somewhere? Where can I buy what I need to start taking care of the problem?

Tl;dr: Coyotes abound, need dead, how I make dead?