I'm afraid this is not a very good idea. If you try to use black cotton dye on something that is only 50% cotton, the result will be a medium gray.

It's easy to dye 100% cotton to black and other dark colors, but there is no dye that can color both cotton and polyester. Any dye that works on polyester will wash right out of cotton, while any dye that works on cotton will wash out of polyester. 

It is possible to dye both the cotton and the polyester by using two different dyes, but at this point you're talking about going to a lot more trouble. All polyester dyes require extensive boiling of the fabric with the dye in order to take the color; you will have to invest in a very large cooking pot, for about a hundred dollars, to be used only for dyeing, since pots used for dyeing fabric should not be reused for food preparation.

There are several companies that will be happy to redye any natural fiber for you, but the only one I can think of that will dye polyester is Manhattan Dyeing Service. See my page on "Where can I find someone to dye my clothing for me?".

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