Over at Bellows and Strings, blogger Luca Selano has made a great post on cross-chording techniques applicable to the D/G accordion. Included in the post are some terrific charts and diagrams.
"Cross-chording" is a term used to describe when a player "crosses over" and takes notes from a different set of bass buttons to get chords and textures that are not native to the tuning system. For example, G/C instruments are not furnished with a button for playing the G7 chord, only G major. But the G7 chord can be played by crossing over and borrowing the adjacent F note while still holding the G chord.
If you are frustrated by the limited choice of notes and chords in the left hand of your accordion, I recommend reading his post. The information isn't limited to D/G instruments - the principle holds true for all instruments with rows that are a 4th apart (G/C, A/D, B/E, C/F, etc.). Simply transpose the notes and chords by the appropriate interval to fit your tuning system.
The rest of Bellows and Strings is filled with more useful information and enjoyable reading, so be sure to browse around for a while.