Starting from the Ruined Lifeguard Shack going South and taking the boat to the other side of the island you will find the quest giver for "The Coconut Bum" quest.
An old man who has gotten his coconuts stolen by kids from the island. Your goal is to find these coconuts to prevent him from laying hands on set children.(Note: These coconuts only appear once you have accepted the quest and cannot be seen beforehand.)
Here are the locations:
West of the quest giver is an NPC in blue clothing next to him is the coconut.
South East of the quest giver is another coconut underneath a tree to the East of an elderly NPC.
The next two coconuts are on the other side of the island.So anything i say from now will be based on the asumption that you have already gone to the other side of the island using the Ruined Lifeguard Shack as a base.
Your next coconut will be next to a female NPC clad in purple armor. She is South of the Ruined Lifeguard Shack pass the Slaver/Goods Seller next to an unlit pile of wood.
The final coconut is located underneath a tree to the east of the Ruined Lifeguard Shack.
Right now (Revision 5309) there is no reward for this quest he agrees to keep his hands off of the children after your character threatens him.