@fBoyle-- Yes, there are eyebrow tints and other cosmetic products on the market that you can use to tint your eyebrows. But most people use these to color their eyebrows in matching shades to make them look fuller or more defined. If you are wanting to change the color of your eyebrows completely, you might have more luck with an eyebrow tinting kit or lightening kit.
I understand that you are not fond of dyes. So you could try eyebrow mascara which is basically a tinted gel product that comes with a mascara type wand. Or you can try an eyebrow kit that includes wax and powder. Or you could go the traditional way and try to color your brows with an eyebrow pencil.
If you are looking for more permanent solutions, then there are also eyebrow tattoos and semi-permanent tattoos which use henna.