Heat oven to 350° F. In a small bowl, whisk together eggs, milk and vanilla.
In a medium bowl, whisk together 2 1/2 cups flour, baking powder, lime zest, and salt. Add sugar and coconut, and stir to mix. Make a well in the center, and pour in egg mixture. Gradually mix with dry ingredients until just combined. Add melted butter, and stir until smooth. Do not over-mix.
Line an 8 1/2- by 4-inch loaf pan with parchment paper. (You may need to prepare a mini loaf pan or other small vessel in the same manner.) Pour batter into pan, making sure it isn't filled more than 3/4 full. Bake until a toothpick inserted into center comes out clean, 1 to 1 1/4 hours, but start checking after 45 minutes. Cool in pan 5 minutes, remove bread from pan, and finish cooling on a rack.
To serve, cut into 8 to 10 thick slices. If desired, toast lightly and spread with butter or lime curd.