You can ride the railroad from Atlantic City to Newark (Liberty) Airport.
Rail Map:
http://www.njtransit.com/images/railmap06.jpg
You will have to transfer from train to train, it will take four trains to get you there.
Atlantic City to Philadelphia: on New Jersey Transit
Philadelphia to Trenton: on SEPTA (SouthEast Pennsylvania Transportation Authority)
Trenton to Newark Liberty Airport Station: on New Jersey Transit
Newark Liberty Airport Station to Airport Terminals: on the Airtrain Monorail.
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Alternatively, you could ride Amtrak from Philadelphia to the Newark Liberty International Airport Station.
There is a short monorail ride from the Liberty International station to the airport terminals, IIRC the fare is $7.00 for the monorail.
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Here's a sample itinerary from the website, from Trenton to the airport:
Itinerary Planning Results
Bus, train and light rail schedules are typically loaded two weeks prior to the effective date. For itineraries more than two weeks in advance, please reconfirm travel times prior to your trip.
Here's Your Best Route
Itineraries from TRENTON RR STATION ***ACCESSIBLE*** to LIBERTY INTERNATIONAL AIRPORT
ITINERARY - 1
Depart: TRENTON (08608)(On NEW YORK PENN STA. [33RD & 7TH ENT])
11:10 AM
Arrive: NEWARK AIRPORT RAILROAD STATION (07102) 12:09 PM
Transfer
Depart: AIRTRAIN STOP NJT RR STATION (07102)(On NIA TRAM NEWARK AIRPORT AIRTRAIN)
12:20 PM
Arrive: AIRTRAIN STOP TERMINAL B (07102) 12:30 PM
REGULAR FARE CHILD/SENIOR/DISABLED FARE
Bus Fare $0.00 Bus Fare $0.00
Rail Fare $8.50 Rail Fare $3.75
Access Fee $5.50 Access Fee $5.50
Transfer Fee $0.00 Transfer Fee $0.00
Total $14.00 Total $9.25