In a large saucepan, combine the orange juice with the 2 cups of water, the granulated sugar and rum and bring to a boil. Simmer over moderate heat until reduced to 1 1/2 cups, about 30 minutes. Add the cinnamon and simmer for 5 minutes longer. Pour the sauce into a heatproof bowl or pitcher.
Pat the mangoes dry with paper towels. In a large bowl, whisk the flour with 1/2 cup of confectioners' sugar, the cornstarch and the 1 1/2 cups of ice water until smooth. Whisk in the coconut.
In a large saucepan, heat 1 inch of oil to 375°. Dip 4 pieces of mango in the batter and add them to the hot oil. Fry, turning once, until golden, about 2 minutes per side. Drain the mango fritters on paper towels and repeat with the remaining mango. Transfer the fritters to a warmed platter and dust with confectioners' sugar. Serve with the sauce and crème fraîche alongside.