The things I know of to color hair naturally are henna, coffee and indigo. I'd google these to see if it's something you'd want.
I personally use henna RED, but you'd most likely have to mix henna with indigo or coffee in order to get a darker color.
You can buy premixed hennas in different colors.
Henna will not bleach your color out and turn it red. It will lay a red color over your existing color. If your hair is black, the result will be black with a red shimmer or you may get no color change at all. If your hair is brown, you'll most likely get dark brilliant auburn. If your hair is blonde, you'll get orange - think Lucille Ball.
