What I've used before is a common sticker remover called "Goo-Be-Gone". Just apply the goo-be-gone to a clean towel and rub the stick spot until the residue is gone. Always work in a well ventilated area so that the chemicals are less likely to enter the slab and more likely to evaporate into the atmosphere. Another option is the solution that auto body shops use to remove bumper stickers from cars. It works the same way as goo-be-gone and you should take the same precautions with its use.
I've used it many times to remove sticker residue from all kinds of plastic, with no adverse results. Just don't let it sit too long, use a soft cloth, and wash the item with soap and water to get rid of any petroleum residue. DO NOT try this on a coin!
The way that I personally have removed sticker residue from slabs or from lots of other things like CD cases (where they put that dumb seal on them) or the bottoms of glasses when you buy new drinking glasses is to use tape. Make a small loop of tape around a couple of your finger tips with the sticky side out, then use it almost like you are dabbing a cloth. Press it against the residue then pull up quickly. Keep dabbing it like this and it will take the sticky stuff off. I usually use scotch tape for this. It works well and you don't have to mess with any liquids.
