tomatoes are from the nightshade family, it is not a good idea to let your birds eat the green tomato as they contain the same poison as nightshade also the plant is toxic, too much will kill your birds.
try sitting them in a shallow pan of water and Epsom salts twice a day , also they could be getting too much protein, mine usually will get all purpose crumble and I will go out and find some wild grass such as young chickweed, make sure to cut it up into small bites, I also keep a shallow dish...