Green snakes are insectivores mainly dependent on insects such as caterpillars, grasshoppers and moths. In case you are looking for the best food for a green snake, go for crickets because they will give your snake the best diet.
1 Additional Answer
Rough green snakes and smooth green snakes have almost identical care and feeding requirements. They will eat grasshoppers, moths, crickets, earthworms and spiders. You can find more information here: http://www.uga.edu/srelherp/snakes/ophaes.htm