Hi, Steve. Have you thought of learning to juggle bowling balls? That should get your downstairs neighbor's attention they way they have gotten yours.
The problem is very simple, the fan is out of balance, but finding the solution can be a chore. Your neighbor can probably tell by looking that it is out of balance but cannot tell which blade or blades are heavy or light. You might be able to take the blades off one by one and weigh them on a very accurate scale, then add weight to make them all exactly the same. An easier way is to tape a nickle to one blade and see if it gets better or worse. Keep moving the nickle around from blade to blade until the vibration gets better. When you find out which one is light, add more nickles as long as the vibration keeps getting better. When it gets worse, take one off. You want to add the weights as far out the blades as possible and tape them securely so they don't fly off.
If all else fails, complain to your landlord and have him do it.