Preheat the oven to 350 degrees. Generously grease and flour a 9 x 5-inch loaf pan.
Whisk the eggs, sugar, and oil in a large bowl until well blended. Whisk in the buttermilk and coconut extract.
Sift the flour, baking soda, baking powder, and salt onto a square of wax paper (or stir in a bowl). Add to the egg and sugar mixture and stir just until blended; do not overmix. Stir in the coconut.
Pour the mixture into the prepared pan and bake for 45-60 minutes, or until a toothpick inserted in the center comes out clean. Remove from the oven and place on a cooling rack.
Meanwhile, make the glaze: Stir in sugar, water, and butter in a small saucepan and bring to a boil. Simmer for 5 minutes.
Pour the glaze over the bread while still warm in the pan. The bread will absorb the glaze and may sink as it cools. Slice the bread in the pan and serve.