I think that there are several choices when it comes to this, but I think that the most "hopelessness color" would be dark gray, not black, because gray already seems sad, and being close to dark would give it a dark mood. Black, on the other hand, is just..... black. I don't think it has much to say for itself because all you can see is dark pits of black. Dark gray, though, it might give you a spark of hope, then seeing the color gray could make you loose that hope.
This is just my opinion, but I hope you like it and I hope it helped!