Flooring Tile - flea market find

I recently discovered a really great coffee table/end table set at a local flea market--great size, even better price---but the tabletop surfaces, which appear to be marble, are a horrible mixture of colors. Can polished stone surfaces be roughed up and painted or stained in any way? ANY suggestions would be appreciated.

What a fun project! Once you get the finish off of the the table top, if there is any left or it may have been a polished finish, you can do a few things to the stone. Staining is an option but painting is really not. If you are able to get to the bottom side of the stone to practice you cout see what astain will look like before you try the top. You might also try buying a peice of marble from a tile store and experiment with it before you try the table