16 or 28 ga double barrel coach gun if you can find one. Or a .410 double. I doubt she will be able to handle the recoil of a 20ga double.
She needs to try a double action revolver to see if she can pull the trigger and hit anything with it. If she can, S&W makes a .22 magnum revolver that might work great for her. Taurus maks the 941 light weight .22 magnum revolver, review of it here Taurus Model 941 Ultra-Lite .22 Magnum Revolver but the trigger pull on the Taurus may be way to heavy for her.