I like it when old silver coins look like that - it gives them character, kind of a "poor man's cameo", with the details stand out better on the black background. Removing it might make it look "cleaned", which would definitely affect the value.
It depends on what the black stuff actually is. Take a good, close look at the black areas with a magnifier, particularly looking at the transition areas from black to metal. Does it look like the black areas are smooth and flat, like a discoloured part of the metal itself? If so, then it's silver tarnish, and nothing will remove it that won't give it that dull, "cleaned coin" look.
If, however, it looks rough and uneven, like the black is kind of adhered to the surface, then it's dirt, grime and goo the coin has picked up from people's grubby hands in circulation. Soaking it in acetone, alcohol or even soapy water should remove it, without causing undue harm. The coin might, however, look "shiny" underneath the grime, creating the reverse effect of what you see now, with shiny metal in the fine detail and dull tarnished metal in the open fields.
