Beet juice or strawberry juice can make a nice pink frosting, but bright red is hard to acheive naturally. Natural dyes aren't quite as vivid, and if you use too much, it's just too much liquid in the recipe. Simply use brightly colored juice as part or all of the liquid in the frosting recipe. (BTW, frosting is simply powdered sugar, butter or margarine or coconut oil or shortning, and a little milk, water, or juice so it's not too thick.)
I don't have a gluten-free cake recipe on hand, but you can take any cake recipe and substitute the following for each cup of flour:
1/2- 3/4 cup white rice flour
1/4 to 1/2 cup starch (potato, corn, or arrowroot, etc.)
1 teaspoon xanthan gum (or any other dry vegetable gum.)
If the cake recipe calls for milk, you can substitute water, rice/soy/almond/etc milk, or juice. If it calls for butter, you can use any vegetable oil or mixture of oils (liquid or solid).
