Preheat oven at 350°. Lightly butter two 9-inch round cake pans. Line bottoms with a circle of lightly buttered waxed paper. In a bowl, using a fork, stir flour with coconut,baking powder and salt.
Using an electric mixer, beat butter with sugar until light,occasionally scraping the side of the bowl, 3 minutes. Beat eggs,once at a time,until evenly mixed,then beat in vanilla. With mixer on low,add flour mixture in 2 parts,altering with coconut milk.
Divide batter between prepared pans. Smooth tops. Bake in centre of preheated oven until cake tester inserted into centre of cakes comes out clean, 30 to 40 minutes.Remove pans to racks. Cool 10 minutes, then turn cakes out onto racks. Turn top side down so cakes will be flat, for easy icing. Cool.