Being serious, if you are sure the contest is 'if you were going to be stranded on a desert island (1 palm tree and a little spit of sand just big enough not to be covered by water at high tide type), which six things (assumeing 'things' are limited to single items) would you most desire to have droped with you to help you survive and get rescued.' and not 'If you were to visit a desert island (1 palm tree and a little spit of sand just big enough not to be covered by water at high tide type) for the day, which six things (assumeing 'things' are limited to single items) would you like to take with you for fun and convenance for the day.'
1. A manual survival desalinator
like this one but I'd do further research to find out exactily which one would be the best.
2. Satphone or PLB, whichever further research would prove to work most reliably in the middle of the ocean assuming no SAR operations will be underway for you or if they are, they are way off, so that rescue is expedient.
3. Favored shelter, I'd go with a tent of some kind over a tarp, you don't waste a spot on cordage as its included and has poles and it works better on rain if a storm comes up, you can work at half burying it if you think it will go someplace (remember you only have the one tree)
4. Food, eather as big a container of compact survival rations as you think they would allow (case, crate, cargo container), or a fishing net (forget the rod and reel) to catch small fish just past the surf
5. A solar reflective oven to cook the fish, one palm tree would not provide enough fuel for a fire for long
6. a good knife, mostly for cleaning the fish or if you go the ration way maybe a solar panel to keep the batteries up on your PLB/Satphone.
Things to think about:
I am not sure, but I don't think a single coconut palm can produce coconuts, I think they need more then one tree to produce them. I have also heard, that if they do produce, they produce a little less then one a day, although this I am very unsure is true.
GASP, think about not haveing a knife?!? With this setup and the extremely limited resources on the island, while I don't like the idea of not haveing one, I think its usefulness would be severely limited.