The Food Network's frosting chart recommends using 150 drops of red food coloring per 1 cup of frosting to make raspberry red frosting. According to McCormick, 20 - 25 drops equals 1/4 teaspoon, so this is approximately 1 1/2 teaspoons.
When using store-bought white frosting, The Food Network recommends using slightly less food coloring. In the case of red frosting, the recommendation per 1 cup of store-bought white frosting is 111 drops, or a little less than 1 1/4 teaspoons. The Food Network suggests to add the food coloring a little at a time until the desired color is achieved.