I wouldn't consider putting oil in a wooden instrument. I was thinking perhaps beeswax or graphite, or hoping breakin would solve it. It's a Bon Cajun and I will be sending it in for tuning soon so will ask Larry to look at it, but was wondering if this was a common problem with an easy fix.
If the squeak is on the bass side. (very common on Larry's instruments), making a small adjustment to the spring will solve the issue.
The moise is caused as the coils of the spring rub against each other. On the bass springs, there is only one coil.
If you are handy and don't mind opening up your accordion, it is easy to fix. If the idea of opening up the accordion is scary, have Larry, or an accordion repair tech fix it for you.
Assuming you want to do this, once you have the accordion open and have removed the base box (the left hand handle) You can see the simple, hand made springs that are used. Very cool, just a piece of bent spring steel!
Take out the spring and use a knife to spread the coils ever so slightly apart. "Wa-la! no more squeak. This will not affect the spring tension of the spring on the bass springs the way it will on the treble springs.
Play louder... and hopefully the neighbors will know the difference! If you ask me, "Squeaky Springs" sounds like a great song title... or a razorback infested ditch in Arkansas! It's all good!