Thanks!

Can it be subjected to heat? If so, all-purpose dye will dye both the cotton and the nylon in one step, if you add the vinegar required by the nylon. The results will not be washfast until you apply a cationic dye fixative such as Retayne. Read both of these pages:

http://www.pburch.net/dyeing/allpurposedye.shtml
http://www.pburch.net/dyeing/FAQ/fixative.shtml

Fiber reactive dye, such as Procion MX dye or Remazol dye, can be used and gives much more permanent results on cotton, but it requires two separate steps: one at a high pH, with soda ash, for the cotton - see http://www.pburch.net/dyeing/howtodye.shtml
for more information on that - plus another step at a low pH with heat, to dye the nylon - see http://www.pburch.net/dyeing/reactivedyesprotein.shtml

Note that dyeing black requires two to four times as much dye as is recommended by the manufacturer. All-purpose dye often makes colors that are not quite black. Fiberr reactive dyes on nylon may result in an off color, too, such as olive green. The best black dye for nylon is Lanaset black dye, from PRO Chemical & Dye, but it will have no effect on cotton. The best black dye for cotton is either the MX Cotton Black, sold by PRO Chemical & Dye, or their black Liquid Fiber Reactive Dye, which is a Remazol type dye - see http://www.pburch.net/dyeing/remazol.shtml . Remazol black should also make a good black on nylon, since it is that rarity among fiber reactive dyes, a single-hue unmixed black, and thus should come out the same color on different fibers.

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