Stardew Valley created by ConcernedApe.
Images used for educational purposes only.

You’ll trigger this quest on the 19th of Winter in your second year. Some mail will arrive in your box from Gus. Gus needs a Coconut something fierce. Hook him up.

The primary method for snagging a Coconut is to go hunting in the Calico Desert. The Desert is only accessible via the bus, which is broken when the game begins. You need to repair the bus via the Community Center Bundles or via JojaMart, if you decided to purchase a JojaMart Membership. Both methods will cost you over 40,000 gold to achieve, so expect a lot of setup before you can complete this quest.

Once the bus is repaired, head to Calico Desert. Coconuts are common forage items that appear at random. Grab one and take it to Gus in the Stardust Saloon, where he spends the vast majority of his days. He’ll give you 600 gold via the Journal.