Monkey nuts heal 200 life points. They can be purchased at Solihib's Food Stall on Ape Atoll after starting the Monkey Madness quest. Players must be in the form of a monkey (by holding any monkey greegree) before talking to the stall owner or they will be thrown in jail just like in the quest.
During the 2012 Christmas event A Stray In A Manger, players could randomly obtain monkey nuts by catching a snow impling or by unwrapping an active Gift of Giving. It was even possible for a free player to obtain this members object via this method.
Monkey nuts is a colloquial term for a number of nuts, including peanuts.