Bring first 6 ingredients to a boil in a small saucepan over medium heat. Remove from heat; stir in vanilla.
Cover and let stand 30 minutes. Pour syrup through a wire-mesh strainer into a small bowl, discarding ginger and spices. Cool completely; chill.
Combine sectioned oranges and pineapple in a large bowl. Gently stir in chilled syrup. Spoon fruit and syrup into individual dessert dishes. Sprinkle with coconut, and top with cherries.
Make-Ahead Note: Prepare fruit. Seal in a zip-top freezer bag, and refrigerate overnight. Cover and chill ginger syrup overnight. Combine fruit and syrup before serving.