Preheat oven to 350.
Grease two 9-inch loaf pans or one 10-inch bundt pan with butter and dust with flour; set aside.
Sift together flour, baking powder, and salt in a medium-size mixing bowl; set aside.
In a separate bowl, combine mashed banana, milk, rum and lime juice.
In your mixer's bowl beat butter on medium-high until light and fluffy.
Slowly add both sugars and vanilla, and continue to beat until thoroughly combined and no lumps appear.
Add the eggs one at a time, beating each egg until well incorporated.
On low speed, add the flour mixture to the butter mixture alternately with the banana mixture; beat until well incorporated.
Pour batter into prepared pan(s) and top with shredded coconut. *If using a bundt pan, sprinkle the shredded coconut onto the bottom of the pan before pouring in the batter.
Bake for 45 to 55 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Cool in pan for 10 minutes.
Remove from pan and cool completely on a wire rack.