I also made 2 baby slings with fabric that I hand-dyed. The first is an organic cotton twill which is very soft and cozy, but was perhaps a little too thick for pleating and running through the rings.
The second is an Essex linen/cotton blend. I know this fabric is popular with a lot of modern quilters, but I've never used it before. I may have to dye more and use it for a quilt in the future.