Preheat oven to 350 degrees F.
Thoroughly grease and flour two 6-inch round cake pans.
Crack the eggs and separate the yolks from the whites. Put the whites in metal mixing bowl and beat until soft peaks form. Set aside.
In a mixing bowl, beat the butter and sugar until creamy. Beat in the egg yolks and the vanilla, then beat in the cream of coconut.
In a separate bowl, stir together the flour, baking powder and salt.
Add the flour mixture and the milk to the batter alternately, stirring by hand just until flour is incorporated. Stir in the coconut.
Fold in the beaten egg whites.
Pour the batter into the pans. Set pans on a rimmed baking sheet and bake on center rack for about 40 minutes or until cakes appears set and springs back when touched. Let cool completely on a rack.
Split each cake into two layers, then frost and stack to make a 4 layer cake.