A green bananer refers to Exhibit A : a male or female who fails to get action. Hence, the banana (Exhibit B) being pursued is unpeeled by the eater (Exhibit A) and thus the banana (B) is too ripe.
"Justin is a true green bananer, that kid hasn't been laid in a year!"
"Watch out Izzy, that guy's a green bananer. He won't last long...."