Combine cantaloupe, honeydew melon, peaches, oranges, strawberries, mangoes, kiwis, blueberries, and raspberries in a large bowl.
Whisk cream, confectioners' sugar, and rum together in a bowl until smooth; fold in marshmallows. Pour cream mixture over fruit and toss to coat. Cover bowl and refrigerate, stirring frequently, until chilled and flavors soak into fruit, 8 hours to overnight.
Spoon fruit salad into serving bowls and sprinkle with coconut.