Depending on the color of the wood and how bad the damage is you can buy markers at places like Home Depot to fix scratches and little discolorations.

Is the finish on the under side or non visible parts as well? Is it a lacquer finish? If so it may be fixable by reamalgamating. Test this in a non visible spot. First clean the whole area with mineral spirits and a 0000 steel wool pad and wipe up any excess with a rag or paper towels. DON'T use this stuff as it will leave a milky residue. (I learned that the hard way) Then, with a new steel wool pad dipped in lacquer thinner apply and 'brush' the lacquer thinner out in wide strokes following the grain of the wood. Work quickly as it does dry relatively quickly. This will temporarily liquify the lacquer and redistribute it to cover the spot where it's missing. Here's a page that goes into more detail. And again, check a non visible spot first to make sure it won't damage the finish more. There is a product called restor-a-finish, which I believe is the same thing. Never used it but may work as well.

I don't have any advice for you, but I feel your pain. This is the exact reason why my coasters sit in a very odd place on my coffee table. Nail polish remover is a bitch.

You don't tell us your level of skill with refinishing wood. Unless you've done it before, I'd take some pics and seek some expert advice. As for the advice rainarana provided, I'd get permission from the table owners before doing anything.

There's a ring about the size of a quarter etched into my old dining room table from just this very thing. :( I don't think there's an easy fix, unfortunately. I think I'd consult an expert as well.

Ugh, I feel your pain. I also had this happen with one of those oil air fresheners and it ended up a huge mess. If it's a small area, I think one of those pens is your best bed.

Talk to your cousins and see what they want you to do. They might want you to fill the spot in with one of those wood-tinted pens, they might want you to refinish it, but don't do anything without their permission.

If you know where they bought it, call the store and ask for advice.

Don't try anything - just tell them you did it, that you're really upset/sorry about it, and ask them how they'd prefer you make it right.

This! There isn't an easy way to fix this. This happens to the best of us. I had some vanilla extract leak on my table and eat away a nickel sized patch of finish. Talk to your cousins and help them figure out how to make it right.

And I don't say this to lecture, but in the future, stay away from anything that can't be damaged, even if you take precautions. I have definitely learned this the hard way myself.

This. And be prepared for a professional fix - in fact, I'd start finding a furniture restorer now and getting quotes. This is not something to try to fix yourself.

Actually I've seen a stain at home depot that is specifically for fixing small mars like this, you don't have to strip and restain the whole piece of furniture, you can rub it in to the affected area and it's supposed to blend in with the rest. I forget what it's called, though :( If you go to the paint dept hopefully a staff member can help you find it!

good luck!!

My daughter dumped an entire bottle of nail polish remover on our new table last year...I used some old English to cover as much as I could and then got a nice table runner til we could buy a new table. Good luck