Preheat oven to 350. Add ½ cup of dark rum and ½ cup of raisins to a sauce pan. Boil for 5 minutes, then turn off the heat. Let them sit and absorb the rum while you prepare your other ingredients.
In a mixing bowl, add 1 cup flour, 1 tsp. baking soda, ½ tsp. baking powder, ½ cup granulated white sugar, ¼ cup brown sugar, 1 tsp. cinnamon and ¼ tsp. salt. Whisk together.
Chop the carrots in a food processor or grate them until you have 1½ cups of grated carrot. In a separate mixing bowl, stir carrots and ⅔ cup oil until nicely mixed. Then, add the ingredients in your other bowl and the rum raisins to your carrots and stir. Add 2 beaten eggs to the mixture and stir until you have a nice batter.
Grease a cupcake tin with butter and fill each cup half way, making sure to evenly distribute the raisins between the cups. Bake for 12-15 minutes (or until edges are brown and the tops are spongy and not sticky).
While the cupcakes bake, make your frosting. In a mixing bowl, add 8 oz. of cream cheese, 8 tbsp. of softened butter, 1¼ cups of powdered sugar, 1 tsp. of real vanilla extract and 1½ tsp. of coconut extract. With a hand-mixer, whip the frosting together until nice and smooth.
Check to make sure your cupcakes are done. When they are, let them cool for at least 20 minutes, then frost and serve.