Don't laugh, and I haven't tried it on any corrosion as severe as yours, but ketchup and a little salt cleans copper coins extremely well.
It wont get rid of the black gunk, but works just as good as regular polish as a cleaner (minus the abrasives that will get the black off). But leaves them clean and dull.
Make sure you rinse the coins good and completely dry them or the malachite tarnish (green) will be back pronto. Historians claim it adds character to things like our Parliament Buildings, but somehow that doesn't hold true for coins and cups.
The best thing for copper, is copper polish. Vingar and salt are just going to clean it well enough to get an instant dull pink tarnish once it's removed from the solution. But a copper polish used properly will give it that nice copper shine.
By the way, do not mix coins of different metals (ie copper and silver, or your copper/silver coin) or you risk ruining them forever. By combining metals in an acid solution, you're basically creating a battery in the simplest form, and will electroplate the coins with interestng results. Same goes for putting your metal cup sets in the dish washer.
It's permanent. Can't buff that stuff off. Heh.