Preheat oven to 350 degrees. In a large mixing bowl, cream shortening and brown sugar. Beat in eggs. Combine the flour, baking soda and salt. Gradually add to creamed mixture. Stir in rhubarb and coconut. Drop by tablespoonfuls 2 inches apart onto greased baking sheets. Bake for 12-15 minutes or until lightly browned. Remove to wire racks to cool.
For Frosting: In a mixing bowl, beat cream cheese, butter and vanilla. Gradually beat in the confectioners' sugar until smooth. Spread over cooled cookies. Store in the refrigerator.