Preheat oven to 180 degrees. Combine flour, desiccated coconut, sugar and yeast in a large bowl. Add egg and 1 1/4 cups luke warm water; stir until combined. Using hands bring dough together. Turn onto lightly floured surface. Knead for 10mins. Put dough in a lightly greased bowl. Cover with glad wrap: put in a warm area to rise for an hour or until it has doubled it's size. Line 2 trays with baking paper. Punch dough. Knead for 1-2mins after risen. Divide into 12. Place on trays ( cover with damp tea towels; place in a warm area for 20-25mins. Brush tops with egg yolks and a tablespoon of water. Bake for 25mins or until golden brown. Transfer to a wire rack.
Sift icing sugar into a medium bowl. Add butter and gradually add 3 tablespoons of water while stirring. Tint icing with dye. Spread icing over buns and sprinkle with some coconut.