I do. I sew my diapers from organic cotton fleece and dye the outside layer with Procion MX dyes. Procion MX dyes are colorfast and gorgeous. Most of the colors are considered 'low impact', avoid turquoise in particular if this is a concern for you. Here is a
link to read more.
Sources for procion dyes include
Dharma Trading and ProChemical on the internet, Jacquard dyes in art stores, and Rainbow Rock or other tie-dye kits sold at Michaels, JoAnn's, etc. You can also use Permanent Dylon dyes. Avoid Rit anything, it sucks.
For more information, Dharma has lots of directions, as does
Paula Burch's site on fabric dyeing.
Procion MX dyes are, IMO, the safest and easiest dyes for diapers. Most hand dyed WAHM diapers are dyed with Procion MX dyes. But if you want to look into using natural dyes,
Paula Burch has a nice overview with resource links on her website.
HTH!