Combine flour, sugar, coconut, pecans, baking soda, salt and cinnamon in a large bowl. Combine oil and eggs; stir well. Stir egg mixture, grated carrot and pineapple into flour mixture. Spoon batter into a 13x9 baking pan coated with cooking spray.
Bake at 350 degrees for 35 minutes.
To make frosting: Combine butter and cream cheese in a bowl; beat with mixer at medium speed until smooth. Beat in powdered sugar and vanilla until just smooth. Spread frosting over top of the cake. Garnish each serving with grated carrot.