One trick that players of piano accordions with less than a full set (Listen JiK - I'm talking about the INSTRUMENTS, not the PLAYERS :-P) of bass buttons do is to 'fake' any '7th' chord by just playing the chord itself, in much the same way as Jim suggests. The note with the pitch of the '7th' SHOULD be somewhere in the tune (orif some other instrument like a guitar is playing along) if it is really all that important.

I was trying to find it, but I'm not at home right now: there is a site out there which shows how to generate extra chords with combinations of the Stradella Bass Buttons on a P/A, - there should be a link somewhere in this maze of threads here at Mudcat...

Basically this guy has done all the hard work, but you can 'easily' work it out from first principles of music scale theory! :-)