First you have to rule out bad connections and wiring problems.
If they hum more when you get close to them with your fingers you could shield the pickup with aluminium or copper foil and connect to ground. Piezo's are very sensitive for low freq. noise like 50Hz (your body etc.). If your strings are not properly grounded the hum will also increase when you touch the strings. This will be considerably reduced when you put an extra shield like I described.
just been reading your piezo humming problem
I've had this before and solved it by using copper foil shielding arround the jack socket and undre the area where the piezo is fitted.
But, like Ted says, it does seem to be a grounding or dry solder joint problem.
Hope you get it sorted
check solder joints
I agree with opinions that point to the wiring...unshielded wiring invites hum, and piezos typically being high impedance makes it worse.
I guess also double check you don't have the the signal (or 'hot' side) and ground reversed.
I've always wondered what would happen if flat disc piezos were reversed, but the piezo disc itself isn't shielded so I might not be surprised if reversed wiring did NOT make a lot of difference.
Try to put an extra shield around the piezo section of your pickup if that's possible, using conducting tape.
Connect the extra shield to the shield of your wiring as close to the piezo as possible.
This could solve your problem.
If you won't to test is first, just put a grounded piece of foil near the piezo when active, and determine if humm/buzz decreases.
I hope this problem from 5/9/2010 has been solved by now