Green bananas are items used during the Do No Evil quest. It can be obtained by taking from the crate of bananas in the northwest part of the monkey temple in Marim on Ape Atoll. They are used in the quest to lure the Monkey guard away from the three wise monkeys in order to prove to them that you are human.
Inside the temple, it turns into a Mouldy banana if left on the ground too long and becomes useless at this point. Everywhere else it just appears on the ground and acts like a normal banana. If you drop the banana while a NPC or player is standing on it, you don't see it, as it acts like an NPC (which also has yellow name when right-clicked). This is only when in the area where you have to distract the monkey guard (everywhere else it behaves normally like an item).
It is impossible to get more after the quest, as the Monkey guard continues to stand by the crate of bananas and thwarts any attempt to take any more. Any leftover bananas from luring him to the crate are not taken from the player after the task or the quest is completed. They appear to have no more use after the quest and cannot be eaten.