Well I for one don't like the spit and saw-dust method - far too often I've seen coins damaged by it, but I'm sure that it could be done without hurting the coin.
My personal 'favourites' for getting rid of the black colour are :
a) dunk it in ammonia for a while (i.e some hours)
b) (same principle spit and foil method) - get some washing soda (either by making it from sodium bicarb or buying it from Asda at 69p for lots) put it in a aluminium pan with a a decent amount of water - boil this up. Put coin in it and contiune to boil - I usually do this for about 5 minutes.
Remove the coin and brush with a very worn toothbrush or a horsehair brush. This will leave a nice clean coin.
If you still have any black left on it after then dunk it in some acid - I'm currently using Jeweller's Pickling (which can be bought from Craft suppliers) which is a buffered Sulphuric Acid.
If the above combination doesn't remove the 'black' (although you might need to do the washing soda bit a few times), you might not have a good silver coin.
If that doesn't work then there is alway a brillo-pad
