I can see Kansas City - Independence for 9$
Not cheaper, but Newark Airport to Newark Penn Station at $17 but 5 minutes journey time is around 3 miles.
I made that journey in 2006 when Amtrak had their NE rail pass (which was incredible value for something like $80 for 4 or 5 days unlimited travel) and I remember the conductor telling me of the high price, which was purely to encourage passengers to use the NJ Transit services.