Easy Jet from from Belfast to Glasgow but Glasgow Airport is a good distance away from Prestwick. Would require you getting a bus from the Airport to get on a train from Queen St Station (right next to the bus station) to Prestwick which drops you off at the Airport.
I agree that Ryanair wont accept anything other than a Passport even for Internal.
Easyjet... are supposed to only take Passports or Full Driving Licences HOWEVER I just flew back from Bristol on Sunday and a lady never had any ID on her and they accepted an employee card with her anme and photograph on it. If you have any sort of card with your name and photograph on it that is supplied by someone like a library or learning institution then you should be able to use it (I know they did accept that sort of thing years ago anyway).
I would call up just incase and get someones name who says its ok with a call reference number.
Hope this helps.
P.S. To get from Glasgow Airport to Glasgow City is not that long and nor is the train. Just make sure you have about 1.5hrs- 2hours before test so you can spare time getting lost!!!!