If it's strictly a budget and physical size issue, I'd say Savage, followed by a Handi Rifle or a similar model from Rossi or whoever else makes them.
My Bud's Savage was never much to look at, but it was a frikken laser beam with everything that was shot through it in the gopher patch!
The Handi Rifles always seemed a bit cruder than they needed to be, but are plenty cheap too.
Might be a good time to ask, but does she actually see the coyotes on a regular basis? Because my money is on getting maybe two shots at them before they completely change strategy's around her place, and go nocturnal. Talking with a trapper may be a better idea. Gonna depend a lot on whether there are a lot of dogs in the area too.
Lotsa things to ponder, but if it's gonna be a gun, hard to go wrong with anything that will shoot straight. Any used around?
Cheers
Trev