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Put the cake mix in a mixing bowl and add the butter. Using a pastry blender or 2 forks, cut in the butter until the mixture resembles coarse crumbs. Add the eggs, milk and rum. Beat with a wooden spoon until you form a smooth batter. Fold in coconut until evenly distributed.
Spray 2 madeleine molds with nonstick cooking spray. Using a tablespoon, drop the batter into the molds filling halfway. If you don't have madeleine molds, you may drop the batter on an ungreased baking pan. Bake for 12 to 15 minutes, until the cookies are nicely browned. Let cool in the pan then turn out onto a platter. Repeat method with remaining batter.