We put black slate on the floor of one of our bathrooms. I really love it. That's the only tile in that bathroom, and the walls are painted a really pretty blue (Ben Moore Gossamer Blue). The white pedestal sink and free-standing tub really pop against all that. Love love black slate. Anyway . . . I do not remember the name of the grout we used, but it is very dark-- almost black-- though I suspect it was a dark charcoal gray. But because slate can't be run that close together, the grout lines are wider than they would be if using, say, rectified porcelain. So I'm pretty sure we used an almost black grout color. I would pick a grout color that's closest to the slate color. I think you might be unhappy with a contrast. ?
Mapei is a good grout and offers a wide range of colors, including black and varying shades of gray. See if you can get samples to bring home and check out the grout color, beside your slate, in your lighting.
http://www.mapei.com/US-EN/coloured-grouts-list.asp
Q