Preheat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
In a large bowl, beat butter and sugar until light and fluffy. Add eggs one at a time, beating well after each addition.
Mix in coconut milk, lime juice, and lime zest.
Gradually add dry ingredients to wet ingredients, mixing until just combined. Stir in shredded coconut.
Pour batter into prepared pan and smooth the top.
Bake for 35 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.