Sift together flour, sugar, baking powder, and salt in a large mixing bowl. Cut in butter and cream cheese with a pastry blender until mixture resembles coarse meal. Stir in coconut and apricot preserves.
Drop dough by teaspoonfuls 2 inches apart onto ungreased cookie sheets. Bake at 350° for 10 to 12 minutes. Remove from cookie sheets, and cool on wire racks.