Maybe add some things to the environment like wildlife and waterfalls.
The music is great, it would be nice to hear birds and water as well.
The player's surroundings are important in this game.
Add more hatchets so you can progress further.
Currently if I bring 16 coconuts to the pay-phone it just gives me the same hatchet I got for 12 coconuts previously.
I took falling damage and was unable to do anything about it, so the game could probably have some food items.
Fishing mechanics would be good for this game.
Pineapples or bananas would fit well too.
Or maybe you can just eat the coconuts to heal yourself.
You could also add something more in regard to exploration.
My ideas are:
* Rare coconuts that are worth more. Maybe they are glowing and colorful.
* When you obtain a certain hatchet, new objects begin to appear on the island.
* Maybe a hut appears, then another and eventually the island has transformed into a resort.
* Or perhaps a raft appears and takes you to another island where you start over from the beginning. You are are credited for completing an island, then the islands become part of the progression.
* A mysterious portal could appear that takes you to another dimension, you have to collect coconuts to open a portal back to the original island, collect cocunuts again, then a raft appears, you take the raft and sail off, you have completed the game.