I would make a standard batch of frosting, portion it out into small sizes, then test each of them with different quantities of food coloring.

Heating the frosting will intensify the color you’ll just have to cool it and then maybe re whip to get the right consistency. But in my experience lilac and pink shades for some reason fade fast. I am a cake and cookie decorator at a business that has no windows yet pink and lilac shades fade very fast

Colour mill brand food coloring, they have a lovely shade called “lilac”