Try looking for "getting drink rings off tabletops." That's pretty much the same thing.
Salt, Vaseline, car wax, baking soda, mayo are all recommended, but that's for people who don't have garages and chemicals, I guess. And this seems to be for new stains that still have water marks.
The finish is already wrecked, right? If it is, I'd give the DNA a whack on the smallest spot. If it works, go bigger.
If the DNA doesn't work, try a blow dryer (not too hot) and see what happens.