I have a portable DVD player that can be powered in a car with a
cigarette lighter plug or work anywhere with an AC adapter and 2 prong
plug.  I would like to be able to use the player in places where there
may be neither power source - such as in an airplane.  What are my
options for a rechargeable and small (lightweight / portable) power
supply that can either supply via a car charger or 2 prong plug?

Doubt if you will find a pack with the correct connector but for the
pack itself you could check out 12 volt model battery packs. You?d
have to source a connector too but most audio equipment uses standard
items.

Best