1. Preheat oven to 350 degrees. Grease a 9-by-13-inch baking dish and set aside.

2. In a large bowl, whisk together 1 3/4 cups flour, baking powder, salt, and coconut. In another large bowl, using an electric mixer, beat butter and 1 cup sugar on highuntil light and fluffy. Add eggs, one at a time, and beat until combined.

3. With mixer on low, add flour mixture in three additions, alternating with two additions of buttermilk, and beat until combined. Stir in lime zest and 2 tablespoons of lime juice. Pour batter into dish. Smooth top with a rubber spatula.

4. In a medium bowl, toss together 1 tablespoon flour, 1 tablespoon sugar, berries, and 3 tablespoons of lime juice. Scatter berry mixture over batter. Bake cake for 35-40 minutes, or until cake is golden at edges and a toothpick inserted in center comes out clean.

5. Let cake cool in pan on a wire rack. Cut into squares and serve.