In a large bowl, beat shortening and sugars until blended. Beat in eggs and vanilla. In another bowl, whisk flour, baking powder, baking soda and salt; gradually beat into sugar mixture. Stir in oats and coconut.
Divide dough into 4 portions. On a lightly floured surface, shape each into a 6-in.-long log. Wrap in waxed paper; freeze 2 hours or until firm.
Preheat oven to 350°. Unwrap and cut dough crosswise into 1/2-in. slices, reshaping as needed. Place 2 in. apart on ungreased baking sheets. Bake 10-12 minutes or until golden brown. Cool on pans 5 minutes. Remove to wire racks to cool.
Freeze option: Place wrapped logs in a freezer container; return to freezer. To use, unwrap frozen logs and cut into slices. If necessary, let dough stand a few minutes at room temperature before cutting. Prepare and bake as directed.