Removing Adhesive On Coins

I prefer xylene to acetone, but both should work.

with all of the above, but I can add this:

That 2nd coin appears to be a Greek silver tetradrachm of Alexander the Great around 330BC.

Acetone can also reduce the appearance of PVC. Give the coins in question a looooooong soak--a few days minimum. You can test for effectiveness over this span of time.

The black might be a deposit from the ground, in which case it might not come off without causing damage.

Adhesive by itself easy enough to remove with acetone.
The problem is that adhesives often have sulfur in their formulation, and this can cause blackening on contact with the coin. This sort of thin surface corrosion cannot be removed with acetone.

If this coin has already had a long soak in acetone, all beneficial treatment that can be done, has already been done.

Nevertheless, the advice of travelcoin may help, but there are risks attached, partly dependent on the metal alloy.
These are also the risks that a museum curator would consider, when cleaning ancient coins after recovery from burial.

The black appears to fade into purple in spots which suggests horn silver (AgCl).

Here are the results of the first batch. It was fun to discover what lay hidden under the adhesive!

Ah yes, the wonders of acetone...