I'm going to recommend you go to a good local gun shop or pawn shop and pick up a used rifle with a bit more kick. A .22 rifle does OK on dog/coyotes, but only if you put a good shot in the vitals (best is the nugget), and you're really looking at doing that accurately at a STATIONARY dog around 100' or less for most folks. Moving, you're more likely to just wound him.
Edited by flyingtnh - 9/27/11 at 3:24am
You can pick up a used singleshot shotgun for pretty cheap (heck, new they're around $125-150), but range is a factor there also unless you go with a slug.
Instead, I'd be looking for a .22 Mag at the smallest, but better would be a small centerfire - .223, .243 or .270 would be great.
If you can drum up a bit more, Rossi makes some great single-shot combos that I think are just about ideal for this kind of thing. They come with 2 to 4 multiple barrels, usually some mix of shotgun, .22, and small centerfire. You could also get one of the youth models (slightly shorter stock and barrel) just because it's easier to tote. I've seen these combos for ~$200 at Dick's (sporting walmart up here in the NE). Nice and simple, with iron sights.
When I went to look at the link, I found this that I think might fit the ticket even better, because you could wear it in a shoulder holster, but shooting a large cal handgun accurately requires some practice. http://www.rossiusa.com/product-details.cfm?id=218&category=3&toggle=&breadcrumbseries=
You'd be looking at shorter ranges, but a .45 Long Colt will stop a dog pretty quick.
As far as burying - I'm all about dropping them off with the woman who's been feeding them. If you live someplace like here where it's pretty easy to compost, you could also bring them to the edge of your property and pile a bunch of manure on them - they compost in a couple months.
Edit--- l missed the post where you took care of business. Well, if his friends come back...