Feel free to use pre-grated carrots. (Grocery stores usually keep them near the bagged lettuces.) That's what I do when making carrot cake and it works beautifully.
Coconut Carrot Cake
recipe from 1985 Baker's Angel Flake coconut advertising
2 cups unsifted all-purpose flour
2 1/2 tsp. baking soda
2 tsp. cinnamon
1 tsp. salt
1 cup oil
2 cups sugar
1 can (8 oz.) crushed pineapple in juice
2 cups grated carrots
1 1/3 cups Baker's Angel Flake coconut
1/2 cup chopped nuts (I would use walnuts or pecans)
Mix flour, baking soda, cinnamon, salt. Beat oil, sugar and eggs thoroughly. Add flour mixture. Beat until smooth. Add pineapple, carrots, coconut, nuts. Pour into greased 13 x 9-inch pan. Bake at 350˚ for 50 to 60 minutes. Cool 10 minutes. Remove from pan. Cool on rack.
Coconut Cream Frosting
Toast 1 cup coconut. Cool. Cream 1 pkg. (3 oz.) cream cheese with 1/4 cup butter. Alternately add 3 cups sifted confectioners' sugar. 1 tbsp. milk, 1/2 tsp. vanilla. Beat until smooth. Add 1/2 the coconut. Frost cake; top with rest of coconut.
I still have my first piece of Tupperware, a yellow colander I got in the early 1980s.