How can I deaden the vibration noise of a box fan?
If you can access the bottom of the fan you might be able to wedge something in there to put pressure on the box and stop the vibrations, but I've found that often with fans like this, they only vibrate at certain speeds regardless of how it was mounted.   Something easy and relatively inexpensive you can try is adding a fan speed controller (not a light dimmer!) and turning it down slightly to see if this stops the vibrations.

Side note: If you want a quieter fan, a trick is to buy a larger fan then required and run it at a slower speed.