With a cleaver, make four identical cuts on the top of each coconut, forming a square; then "pop" open the tops using the back of the cleaver blade. Pour the coconut water into a glass storage jar and refrigerate for later use. Now, with a swift chop, crack the coconuts in half. Pry out the coconut meat using the backside of a large spoon. Rinse the coconut meat and pare away any remaining bits of husk. Chop the coconut meat into 1/2-inch squares and transfer them to a medium mixing bowl. Add the lime juice and orange juice and toss to mix.
Add the green onions, tomatoes, cucumber, jalapeno, bell pepper, parsley, cilantro, olive oil, sea salt and cayenne and gently mix to combine. Finally, mix in the avocado. Serve immediately, with tortilla chips on the side, or chill in the refrigerator for 30 minutes to 1 hour before serving.