It depends on the capacity of your cousin...can he/she walk, talk, move in genereal. considering all these factors then u can decided what you can do for and with your cousin.
My grandmother had a stroke and she couldnt talk or move well, all she could say wany her name in different intonations to communicate but i would take her out and drive to a nice place to push her around in the wheelchair, id cooker her food as i thought the homes food was gross xD and well id spend time with her doing nails and hair and id give her a bath if she needed or wanted it.
Again it all depends on ur cousins capacity :)
You could offer help to take care of her home and all the things that accumulate when a person is not at home.
It's bad to be in hospital and worry about all the things that you ought to do and that can go amiss when no one takes care. Fetch her mail, clean her home, do her laundry, look after her kids and her pets if she has any. Mow her lawn, water her flowers and just make sure that she doesn't come home from hospital to find a pile of work to be done.
And when you visit her, tell her that everything is all right and taken care of.
think of things to take her that most people wouldn't think of. For example my auntie is going into hospital so im going to get her like fancy hand creams and like a sudoku book or somthing along those lines, don't get her flowers or fruit. Try pots of custard or sandwiches or even a daily newspaper. When my dad was in hospital the thing that was worst for him was how bored he got, so try and think of things that could occupy her. Get her a book on somthing she's interested in and most important keep in regular contact with her.
Well, what you could do is pray for her. I belive that prayer is the best thing to do.