If you're working on your Island Sanctuary in Final Fantasy XIV, you know you always need to stay stocked up on materials. Not only are they vital to progressing your sanctuary, but they are also what keeps your island generating gil. As soon as you unlock your Island Sanctuary, you'll realize you need to know where to go to stock up on materials.
While you won't need substantial amounts of Island Coconuts, you should still always have some on hand for the few Handicrafts requiring them to generate a good amount of Cowries.
Where to find an Island Coconut in FFXIV's Island Sanctuary
Island Coconuts are found by interacting with Palm Tree nodes on your island. To interact with these nodes, you must first enable "Gathering" mode in the Island Sanctuary menu. Getting Island Coconuts also requires access to the Islekeep's Iron Hatchet.

The best locations on your Island Sanctuary to find Island Coconuts are:
Pristine Pond: This area is where the Sanctuary Gathering Log points as the main location for Island Coconuts (X: 18.2, Y: 24.2), and it is easy to see why. At this location, you'll find ten Palm Trees. You'll only have to hit one additional node to trigger the respawning of your first Palm Tree, and there are plenty of nodes to pick from, making this a quick and easy farming spot.
Screengrab by Fanbyte via Square Enix Coral Sands: If you're looking to combine a few different nodes, Coral Sands is a great option. The area from (X: 29.0, Y: 26.5) to (X: 30.8, Y: 23.5) holds seven Palm Trees, and the beach has plenty of other nodes to add to your farming path. This spot is an excellent choice if you need both Island Hemp and Island Coconuts.
Screengrab by Fanbyte via Square Enix Pirate Bay: The last good option for farming Island Coconuts is on the cliffs by Pirate Bay (X: 16.1, Y 12.8). This area is home to five Palm Tree nodes. There are a few other node types around this area, so you can complete a circling gathering path without much trouble.
Screengrab by Fanbyte via Square Enix