You are going to be pretty safe with trying naptha (lighter fluid) or mineral spirits to try and get the ring off. Make sure you rub with the grain.
I would then go on to Goof-Off but would try it in an inconspicuous spot first. That stuff is pretty amazing.
Can you feel the ring with your finger...is it raised?
The rings black appearance may mean that a fungus has grown there in the past-- perhaps feeding on drink residue. A very week bleach soln would be the answer in that case. But try on very small area first.
We are just in process of having our dining room table completely refinished ($400) to remove surface rings etc.
Try some 600 sand paper and lightly sand a small section and see if it starts to come off. It may just be in the top layer and not actually in the wood grain. I have had similar stains and had good luck getting them off.
I know this is gonna sound strange but, I've seen my mother remove rings from her furniture with mayo........put a little dab on a soft cloth and rub it it and the wipe off. I would try it first in a hidden spot just to be safe.
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