I too had this problem with my "Bon Cajun" accordion. The buzz/rattle was on the bass side, top button, on the push. I sent it back to Larry Miller before he retired so that it could be repaired. It was eventually returned to me with a note stating that they could find no buzzing sound. I then removed it from the case and played it. The buzz/rattle was still there. So frustrating.

I just tried the advice of the earlier poster. I took it apart and noticed that one of the leather pieces wasn't flat like the others. It wasn't flush against the metal portion where the reeds are located. I carefully (it was glued) pulled that piece of leather off. Then I wet the leather, set it on my kitchen table, and pressed a flat piece of wood against it very hard for a while. I did this until the leather looked flat again. I then glued the leather back into place. Voila! No more buzz/rattle! Thank God! It was driving me crazy, lol. It's just a shame that I wasted my time & money in shipping it back to be repaired.