Preheat the oven to 325 degrees F. Line a muffin pan with paper liners. Set aside.
In a small bowl, combine sugar and lime zest. Rub together with your fingers, until fragrant. In the bowl of an stand mixer, cream the butter and sugar mixture together on high speed until light and fluffy, about 5 minutes. With the mixer on low speed, add the eggs, 1 at a time, scraping down the bowl after each addition. Add the vanilla, coconut extract, lime juice, and mix well.
In a separate bowl, sift together the flour, baking powder, baking soda, and salt. In 3 parts, alternately add the dry ingredients and the buttermilk to the batter, beginning and ending with the dry. Mix until just combined. Stir in coconut.
Fill each liner to the top with batter. Bake for 25 to 35 minutes, until the tops are brown and a toothpick comes out clean. Allow to cool in the pan for 15 minutes. Remove to wire cooling rack and cool completely.
While the cupcakes are cooling, make the frosting. In the bowl of a stand mixer, beat butter, vanilla, and coconut extract until creamy. Add powdered sugar 1 cup at a time, alternating with lime juice, beating until combined.
Frost the cupcakes and sprinkle with coconut.