For syrup, in a small saucepan combine water, sugar, lemon juice, and ginger. Bring to boiling over medium heat; reduce heat. Simmer, uncovered, for 3 minutes. Remove from heat; stir in lemon peel. Cool to room temperature. Strain, if desired.
Pour syrup over melon balls. Stir gently to coat. Cover and chill for 2 to 24 hours. To serve, spoon melon balls and syrup into 6 dessert dishes. Sprinkle with coconut. Makes 6 servings.