In a 3-quart saucepan, combine juices, sugar, and grated lemon peel. Add cinnamon sticks.
Bring to a rolling boil, and let boil for 5 minutes, stirring constantly. Reduce heat to low, whisk in the cornstarch/water mixture, and simmer, uncovered, for 10 to 15 minutes. The sauce should reduce and thicken.
Remove cinnamon sticks and let the sauce cool to room temperature.
Meanwhile, cut up your delicious tropical fruit. Make sure that the fruit is very ripe and naturally sweet.
Toss all the fruit and the coconut together in a large bowl. Add the room-temperature sauce and toss gently.
Cover and place in the refrigerator until completely chilled. Serve cold.