I think the pineapples are optional, they are a nice touch.
I based modified the recipe based on one I found on the Internet:http://allrecipes.com/Recipe/Carrot-Pineapple-Cake-I/Detail.aspx
Ina Garten (Barefoot Contessa) also made a Carrot Pineapple cake, the recipe is on the foodnetwork page: http://www.foodnetwork.com/food/recipes/recipe/0,,FOOD_9936_104822,00.html
Mine is mostly like the 1st one, but I took 2 ideas from Ina's which was to add some flour to the walnuts and raisins (this helps it from not sinking to the bottom of the batter), and to use 1 cup of raisins vs 1/4 cup.
2 cups all-purpose flour
2 teaspoons baking soda
1 teaspoon baking powder
1 teaspoon salt
2 teaspoons ground cinnamon
1/2 tsp of nutmeg
1 3/4 cups white sugar
1 cup vegetable oil (I used those minicups of apple sauce to substitute the oil, the minicup is a little less than 1 cup, so I filled the remainder with oil)
1 teaspoon vanilla extract
2 cups shredded carrots
1 cup raisins chopped a little
1 cup chopped walnuts
1 (8 ounce) can crushed pineapple, drained (Ina used fresh pineapples)
Making the cake:
I used a wooden spoon to mix up the ingredients, but as long as you don't use something electric, it should be ok. Roughly 5 carrots should make 2 cups shredded (but you could add up to 3 cups of carrot if you dont use coconut). I used a food processor to make chopping the carrots easier. Most use the grater to grate them. I baked for 40 instead of 45 minutes. Here are the instructions:
Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch pan.
Mix flour, baking soda, baking powder, salt, nutmeg and cinnamon. Make a well in the center and add sugar, oil, eggs and vanilla. Mix with wooden spoon until smooth. Stir in carrots, raisins, walnuts and pineapple.
Pour into 9x13 inch pan. Bake at 350 degrees for about 45 minutes. Don't panic, the center will sink a little. Allow to cool.
To make the frosting:
I used butter substitute and it was fine. I used a little less than 2
cups of confectioner sugar, but you can do this to your taste.
1 (8 ounce) package cream cheese
1/4 cup butter, softened
2 cups confectioners' sugar
Cream the butter and cream cheese until smooth (I used an electric hand blender, the kind that looks like two whisks are attached to something). Add the confectioners sugar and beat until creamy.
Make sure the cake is completely cooled before putting the frosting on
it. Then put the cake in the fridge until you are ready to eat.
Let me know how it turns out.