Grill chicken pieces for 10 minutes on one side and then turn and grill 5 more minutes. Remove from grill and allow to cool a few minutes so that you don't burn yourself. Remove skin and bones and finely chop or grind the meat.
In the large bowl, stir together chicken, juice, coconut, salt, onions, and peppers. Let stand 1 hour. Adjust seasonings to taste. Serve cold or at room temperature wrapped in tortillas.