Painting rolled fondant with food coloring takes some work. If you try to use a water-based food coloring or add water to food coloring when you paint, you will melt the fondant as you brush on the food coloring. You could end up with goopy fondant and a ruined cake. Instead, paint with an alcohol-based food coloring or mix your water- or glycerin-based food coloring with alcohol. The alcohol will evaporate from the fondant after you brush it on, leaving the color behind and no chance for the fondant to dissolve.
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Mix alcohol-based food coloring with vodka to lighten it or mix it with other alcohol-based colors to make new colors. If you're using powder- or gel-based food coloring, mix the colors darker than you need, then mix in some vodka.
Load your brush with color and brush it onto the fondant. Work as quickly as you can, and avoid overworking the same areas with the brush.
Allow the alcohol to evaporate from an area before going over it again with more color, if needed.