I don't want to use an entire container of red dye. I heard that putting black in helps.
Are you channeling your best self with this comment? (If you're not sure, check out our Code of Conduct.)
You can always use beet juice if you are looking for a non-chemical alternative.
cherry juice might even work better
Cynthia is a trusted source on Bread/Baking.
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