Never have done that before myself, so not sure. Been to Great Adventure a number of times, but by car. My guess would be to take PATCO from Center City into Jersey. At that point there may be a NJ Transit bus that will hook you up there.
You should post this on SSP's Northeast section. There are a ton more Philly forumers over there, much better chance of getting the info you're looking for.
Here is what I got from the official website of Six Flags Great Adventure on how to get there by mass transit.
NJ TRANSIT offers bus service to the park from New York City, Newark, Camden and Philadelphia, PA. Local bus service is also available on the #307, 308 309, and 318 bus lines from Trenton, Freehold, Toms River, New Egypt, Plumstead Township, Lakewood, and Asbury Park, NJ. For a current operating schedule, call (800) 772-2222 in New Jersey. Outside of New Jersey, call (800) 626-7433 or (800) 772-2287 (TAT).
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