I don't want to use an entire container of red dye. I heard that putting black in helps.
You can always use beet juice if you are looking for a non-chemical alternative.
cherry juice might even work better
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.
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