I very shortly played around with electrolysis on a couple pennies and they came out really dark. I never did it enough to learn how anyone else was getting good results. Although, its possible I was placing the pennies on the wrong polarity such as in place of the anode vs the cathode. I'm positive it would make a big difference as one draws metal onto the surface and the other breaks the surface down to be drawn onto the other. You would affectively be copper plating whatever your using as the cathode as shown in the pic below. The anode would be the penny, fittingly shown as a piece of copper. This also diminstrates the fact that the penny is eaten down while the elctrolysis is happening. It would also be very important how you attached your penny to any type of wiring, the immediate contact point seems to deteriate or break down faster than the rest of the penny. If you try this method, document your steps and what you use for electrolyte, ect. Each part can have a big influence in the results. If your solution has too much electrolyte it will draw more current and have a harsher affect and work much faster. I think you want to go with a very low current draw and go slow. this can be fine tuned by starting with the anode and cathode far apart in the electrolyte and slowly moving them closer to achieve the desired current draw.
Thats about all I can add to the discussion considering I havn't experimented much with the process. The pic looks much better once you click it, the black background will change to white once clicked.
http://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Copper_electroplating.svg/471px-Copper_electroplating.svg.png