In a large bowl or the bowl of a stand mixer, mix the flour, powdered sugar, 1/4 cup coconut and butter until crumbly. Press into an ungreased 13x9-inch baking pan. Bake for 10-12 minutes, or until light golden brown.
Lime Filling
Beat the eggs with the granulated sugar, coconut, flour, baking powder, zest, and juice until smooth.
Pour the filling over the warm, partially baked crust.
Bake for 20-25 minutes or until the top is light golden brown. Cool completely for about 1 hour. Before serving, sprinkle with powdered sugar and cut into 36 servings (6 rows by 6 rows).