Sqeaky table...help!

I recently started working with a physician, who has a  wooden massage table that I am to work with.  A section of the table can be raised so that a patient can sit up, and there is a wooden shelf built in underneath the table. The problem is that it squeaks terribly. I feel like I am in a creaky boat! I have asked him what can be done, and we have tried tightening the screws, and made the mistake of greasing it with a silicone product recommended by some well-meaning employees at Lowe's, but to no avail. In fact, in researching this I see that lubricating is not recommended for wood. The physician wants to WD 40 it and I said absolutely not ( smell and no ventilation, and it is bad for the wood.) I offered to bring in my own table, but he refuses, saying the table was expensive ( I don't know how old it is,nor can I find a company name on it) and he has no where to put it. So, I need some help here. I have heard that felt placed in-between the wooden pieces may help. Does anyone else have an idea, please? Thanks in advance!