In a medium bowl, mix together butter, confectioners' sugar, and sweetened condensed milk. Mix in the coconut. Roll dough into 1 inch balls, and refrigerate until set, about 1 hour.
Melt chocolate and shortening over a double boiler, stirring occasionally until smooth. Remove from heat when melted, and stir to make sure the shortening is fully incorporated. Use toothpicks to hold the balls while dipping in the chocolate. Set on wax paper to dry.
