The shelf life of coconuts will vary based on your skill (and luck) in selecting them. A pristine, unopened coconut could be fine for 2 or 3 weeks or more, but the tiniest, unseen crack in the shell will start the decay process which advances quickly. In some cases, you won't know the condition until you open it. If you catch a bad one soon enough, you can salvage much of it.

Select nuts that feel very heavy for their size. Shake it - you should hear/feel the water inside. Inspect the shell for any cracking. It's sometimes very hard to see a minute crack, especially on a dark-shelled nut. Check the three "eyes". They should appear sealed and clean. Make your pick - hope for the best. I usually buy more than I need, w/ the expectation of losing some. I buy from a large Mexican grocer at about $1.10 ea. I might also crack an extra one open, check it, and freeze for later use rather than gamble on storing it for very long. Good luck!