I would say the most promising solution would be to explain the situation to the downstairs tenants and offfer to buy them a nice floor standing fan in replacement. You could try vibration-isolating the ceiling fan but I imagine it would still be audible no matter what was done, especially on reduced rpm settings, and would be a waste of time. You could ask if they could use it full speed or not at all, but that's not a certain thing, either.
The buzz most likely is the reaction of the motor to the chopped up power that is fed to it when reduced rpm settings are used.
Good luck. This would drive me out of the place!
Thanks for the input. A floorstanding fan is really really far from a substitute for a ceiling fan, and I think there are other options I'd try first. Also, it's a condo (and one I'm pretty happy with overall) so moving out anytime soon ain't an option

Maybe I'm too much of an optimist, but I'm thinking there could be all sorts of fixable reasons for this buzzing. The fan might be malfunctioning, for one, and replacing/fixing it might solve the problem entirely! Or it may just be a cheaper fan with shoddy assembly, and replacement and/or modified installation could help there too. Rubber gaskets and/or some kind of sound isolating fastener like an RC-1 clip could possibly reduce the sound travel to a negligable level. This is just speculation, of course, but all I know is that there are lots of ceiling fans out there and they're not all this noisy, so there have got to be ways to improve the situation.
Also, I'm pretty sure she is using it at full speed, or at least the second fastest speed.