Line a 9 x 5-inch loaf pan with waxed paper (or grease and flour it), then set it aside. Heat the oven to 350 degrees.
In a large bowl, whisk togather the sugar, melted butter, oil, lemon zest, lemon extract, vanilla extract, and milk.
In a small bowl, whisk eggs and buttermilk until evenly blended. Set the bowl aside.
In a medium bowl, whisk the flour, baking powder, and salt. With a wooden spoon, sitr about a third of the flour mixture into the sugar mixture, then alternately and half of the remaining egg mixture and half of the flour mixture, stirring after each addition just enough to blend. Stir in the coconut.
Pour the batter into the prepared pan and smooth the top with a spoon. Bake on the center rack until a toothpick inserted into the center of the bread comes out clean, about 45 to 50 minutes.
Remove the pan and cool on rack for about 15 minutes, then remove the loaf and place it on the rack to finish cooling. When the loaf is completely cooled, in about two hours, appply the Coconut-Lemon Glaze, if using.
Directions for Coconut -Lemon Glaze.
Combine the confectioners' sugar, lemon juice, butter and lemon extract (if using) in a small bowl. Whisk to blend. The glaze sould be the consistancy of heavy cream. If needed, add more sugar to thicken it or more lemon juice to thin it.
When the bread is completely cooled , spoon the glaze over the bread and immediately sprinkle the coconut over the top. Makes enough glaze for one loaf.