Fruit juices may be good for the body, but the acidity can be tough on even the hardest of materials. Where the body has fluids to counteract the corrosive effects of acids, a natural material even as hard as marble just receives the acid without reacting against it.
A hydrogen peroxide and polishing powder combo -- similar to the poultice mentioned earlier -- might include a tin-oxide compound that works well for sucking up acidic stains, but with acids, the marble finish suffers a bit. While the chemical cleaning will likely work, once the stain is gone, you'll notice that the acid and acid-stain cleanup have dulled the surface of the marble.
Acid stain removal may require a secondary step called rebuffing, which will polish and re-shine the surface with just a little extra wetting, circling and smoothing with a cloth and fine powders or may require some fine drilling and sandpaper finishing for renewed shine.