Well there is one way:
Continental dishes out one-segment first class upgrades on an infrequent basis to disgruntled passengers.
If you get a hold of one of these, then you *MIGHT* be able to upgrade.
Also in the past, you could buy what is known as a "Prestige Pack" for like $99 and contained in this pack used to be several one-way upgrade certs as well as some presiddents club passes and some other useless coupons....I don't believe that they sell these prestige packs anymore. What you can try to do is show up at EWR and goto the service counter. Ask politely if you could buy a prestige pack. If they have them, buy one and ask the agent to see if they can upgrade you.
The catch is that you cannot upgrade until 2 hrs before the flight. Usually most flights are all booked with elites and non-revs by this point. I have successfully used prestige pack upgrades 5-6 times in the past. Good luck!