In reply to toffer:
You could always park it for free in one of the side streets in Digbeth opposite the coach station, but I'm not going to vouch for your chances of it still being there come Friday night. Failing that, there's plenty of small businesses like engineering firms, mechanics etc. around there that probably wouldn't mind a bit of cash in their back pocket in exchange for you leaving the car in a corner of their yard. Worth asking anyway.