I would also be concerned about any paint and proper prep work will adhere to this surfaces.
You might be better off by purchasing new pulls, hinges and other things in the kitchen that would brighten the area and give it more light to draw attention away from the cabinets.
Get a new lighted ceiling fan, install a wallpaper border that is bright and cheerful. Do things like this that are cheap. Remember this is your home, but you are only a visitor and you might want to leave in the next year and your investment is not that great.
If I was your landlord, I would be greatful for your intitve, but I would not want that type of cabinet painted. this is something that he would have to repair after each tenant moves away.