Is it possible to ferment fresh coconut or its water? Has anyone ever fermented fresh coconut or its water and produced an edible probiotic that tasted good and did not make you sick?
In a word, yes.

According to MakeSauerkraut.com (of all places)


  To make fermented coconut water, the sweet water is mixed with a
  culture (milk kefir grains, water kefir grains, whey from yogurt or a
  powdered starter) and left to ferment for 18 to 48 hours in a warm
  place.


There seems to be a lot of recipes out there for such a thing, a quick internet search for "ferment coconut water" should yield more recipes, methods and the like.