Back in the 60s - 70s, I remember beds that would gently rock side to
side in a see-saw motion whenever music was played. Does anyone know
where I can find a bed like this, if they're still made / How they
worked?

Hi there!  

I was unable to locate any information on the bed you are referring
to. However, I did find an interesting alternative that you might want
to check out.  It's called the Floating Bed, and is a round bed that
is suspended from one's ceiling, which gives you the rocking motion
you desire.

The Floating Bed Company
http://www.floatingbed.com/

Good luck with your search!

CSIgirl