How to help my sister?

My sister who suffers from depression just wants a new animal since our old one died, we hardly see our mother due to her job, she's terrified of the world now since two of her beloved things are gone, she wants something to cuddle but our grandma is allergic to cats and dogs and she doesn't believe in the fact that animals can cure depression. She's so jumpy when she's by herself but she's happy when we she's a dog or cat, is there anyway to help her? For how we had our first cat our grandma just put up with it, didn't take allergy medication but kept her distance from the old one.