Cream the butter in a large mixing bowl; gradually add sugar, beating well at medium speed of an electric mixer. Add the cream of coconut and vanilla, beating well. Add eggs, one at a time, beating well after each addition.
Combine the flour, cocoa, baking powder, soda, and salt; stir well. Add to the creamed mixture, mixing well. Stir in shredded coconut and chocolate morsels.
Drop dough by rounded tablespoonfuls 2 inches apart onto aluminum foil-lined cookie sheets. Bake at 375 degrees for 15 minutes or until the cookies spring back when lightly touched. Let cool completely on wire racks.