1. In a large bowl, beat the sugar, oil and eggs until well blended. In another large bowl, combine the flour, baking powder, cinnamon, baking soda and salt; gradually beat into sugar mixture until blended. Drain pineapple, reserving juice; set juice aside. Stir in the pineapple, carrots and coconut (batter will be thick).
2. Transfer to three greased and floured 9-in. round baking pans. Bake at 350° for 35-40 minutes or until a toothpick inserted near the center comes out clean. Cool for 10 minutes before removing from pans to wire racks.
3. For frosting, in a large bowl, beat the cream cheese, butter and vanilla until fluffy. Gradually add confectioners' sugar and enough of the reserved pineapple juice to achieve desired spreading consistency. Tint 1/4 cup frosting orange; place in a small resealable plastic bag. Cut a small hole in a corner of the bag; set aside.
4. Place one cake layer on a serving plate; spread with a third of the white frosting. Repeat layers twice. With orange frosting, pipe carrots on top; add parsley sprig for carrot top. Cover and store in the refrigerator. Yield: 12-14 servings.