In a medium saucepan, bring ginger, sugar, and 1 cup water to a boil over medium-high and cook, stirring occasionally, until sugar dissolves, about 5 minutes.
With a sharp knife, slice off ends of oranges. Following curve of fruit, cut away peel and white pith; cut fruit crosswise into 1/4-inch-thick slices. In a large bowl, combine oranges, mango, and banana. Pour ginger syrup over fruit and let sit 10 minutes. Serve fruit with a little syrup and toasted coconut if desired.
The syrup can be made several days in advance. Add the fruit up to a day ahead.