How to make red frosting

In the same vein as adding black food dye--add a dark berry juice. Also, a SMALL amount of a SWEET balsamic with fruit juice will give your fruit flavored icing both depth in colour and flavor

Either of those would work nicely. Be sure to simmer to concentrate the color and cook off water which could dilute your cake too much without adding the color you want.

cherry juice might even work better

You can always use beet juice if you are looking for a non-chemical alternative.