Hopefully she knows that coyotes don't pose a threat to humans, so I'm going to assume this is about protecting livestock. If not, someone needs to educate her on the non threat that coyotes pose to her person, and the good they do in terms of keeping nuisance animals eaten down.
Shotguns do have pretty reasonable spread at the distances you're likely to engage a coyote. In most cases, probably too much. There's a goldilocks range where the spread is still tight enough to reliably kill but loose enough it can make up for being a few inches off the vitals in your aim. That's going to depend on the load in question and the gun.
But too close and the spread will be negligible, and too far and it will be too great. Either way, the result will likely be a wounded animal instead of a clean kill. I'm all for the necessity of protecting livestock, not for thrill killing or killing out of irrational fear, but whatever the reason I'm not for wounding any animal.
In terms of which shotgun to get her, I would recommend a break action. I'm 5,8 and barely have enough wingspan to be comfortable with a pump. A double barrel 12ga with low recoil buckshot would be my preferred choice. Whatever you get her, make sure she practices with it, and knows what its range limitations are.
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