Ditto the suggestions for a 20 gauge over a .410. But the key is practice. And, frankly, if the goal is protection against coyotes, I don't imagine that she is going to be walking around outside with the20 gauge slung over her shoulder at all times and if she can make it inside to retrieve the shotgun, then she wouldn't need to protect herself anymore from the coyotes.

Regarding the urban coyotes - I live in San Francisco and there are at least 5 coyotes in Golden Gate Park (the largest city park) and several more at other parks in the city. They had to kill 2 of them a few weeks ago because they had gotten aggressive chasing dogs (Presumably, they were protecting their 5 month old pup that was later found hit by a car.)