Preheat the oven to 350 degrees F (175 degrees C). Grease a 12-cup muffin tin.
Combine flour, baking powder, and salt in a bowl.
Beat white sugar and 1/2 cup coconut oil in a large bowl using an electric mixer until light and airy, 3 to 4 minutes. Add 3 tablespoons Key lime juice, 1 1/2 teaspoons Key lime zest, and vanilla extract. Add eggs 1 at a time, beating well after each addition.
Reduce mixer speed to low. Beat in 1/3 of the flour mixture at a time, alternating with 1/2 the milk and ending with the last 1/3 of the flour mixture. Mix until just combined; do not overmix. Pour batter into the muffin cups until about 2/3-full.
Bake in the preheated oven until tops spring back when lightly pressed, 20 to 25 minutes. Cool in the tin for 5 minutes. Transfer to a wire rack and let cool completely, about 20 minutes.
Beat cream cheese and 1/4 cup coconut oil together in a bowl using an electric mixer until creamy and well combined. Mix in 1 1/2 teaspoons Key lime juice and 1/2 teaspoon Key lime zest. Gradually stir in confectioners’ sugar. Frost cooled cupcakes.
Heat a nonstick skillet over medium heat. Cook and stir the flaked coconut until lightly toasted, about 4 minutes. Remove from pan to cool, about 5 minutes. Top frosted cupcakes with the coconut, pressing in lightly.