Too be honest, the cheapest black substrate you are probably go to find is gravel. Check some of the on-line stores or ebay if your LFS are too expensive. The only black sand I have been able to find is either Pure Quartz reptile sand (not the calcium sand) or Black Tahitian Moon Sand. You can mix the Quartz Reptile sand (naturally black not dyed) with your play sand, as the reptile sand can get pricey, but word of caution, the quartz reptile sand is very very fine, and so it can take a long while to fully settle. If you decide to go that route, rinse very well, and when you think you are done, rinse it some more, the more you rinse, the more likely the sand will settle, and definitely do not do straight quartz sand, too light, most likely will not settle. You will have to mix with a heavier sand, ie play sand, which will give you more of a grey colour not really pure black. The other sand option would be Black Tahitian Moon Sand, but it is very pricey (at least in the US), and quite course, so if you have sensitive sand dwellers, it might be too sharp for them. I would not recommend dying it, I looked into that myself, and every product I saw that would permanently dye the sand was not aquarium safe.
Good Luck