Preheat the oven to 350 degrees F. Grease and flour one 9×5 inch loaf pan.
In a large bowl, whisk together the flour, baking soda, and salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat sugar and butter at medium speed until well blended. Add eggs, 1 at a time, beating well after each addition. Add banana, yogurt, rum, and vanilla; beat until blended. Add flour mixture; beat at low speed just until moist. Stir in 1/2 cup coconut.
Pour the batter into the prepared pan and sprinkle with 1 tablespoon coconut. Bake 55 to 60 minutes, or until a toothpick inserted in the center of the loaf comes out clean. Let cool in the pans for 10 minutes before removing loaf to a wire rack on top of a baking sheet.
In a small bowl, whisk together powdered sugar and juice; drizzle over warm bread. Cool completely on wire rack.