The NER filament (hardest finish and lowest stretch) line that I use is now just called their "Classic" three-strand. It only comes in white and black, but I stain the white to a tan shade by dunking it quickly in the "Early American" shade of Minwax oil stain and then rinsing it really well in naphtha and then Dawn and water. It doesn't fade much at all, even after years of exposure. It is not fuzzy like the Spun Classic version, so it is better for lines which don't frequently get hand-held, but it has their lowest stretch characteristics of the available three-strand offerings.
I had originally tried typical fabric dye and found that about all it did was make dirty white line. The idea behind using the wood stain instead was the thought that if you spill wood stain on a T-shirt, you can probably rinse enough out with thinner that it won't make a stiff spot, but you aren't likely to ever get all the color out. On the filament rope, this works well, using a dark brown stain and ending up with a nice tan color after most of it has washed out. On the spun, fuzzy stuff it didn't work, and a shade of unattractive dirty white was about as far as it would go.
It is also possible to untwist the three strands, shave each one into a taper, wax them and twist them back together, making three-strand line which tapers out, rather than being chopped off. I have used this on sail edges in transition from roped sections to non-roped sections, as well as making eye splices or rope grommets which don't have the big and obvious step-down where they transition from two layers down to one layer. I originally wasn't sure that it could be done, since the polyester fibers are so much softer than natural cordage fibers where this was originally done, but with a bit of practice and patience it can work just fine.
Instructions are here:
http://www.frayedknotarts.com/tutorials/rattail.html