It sounds like his article may be of some help to you.... http://www.coade.com/newsletters/oct96.pdf

A Gerb
http://www.gerb.com/en/arbeitsgebiete/arbeitsgebiete.php?&ID=121&kategorie=8

visco elastic damper might be a good choice and could possibly be instaled in the hot displaced condition just check to make sure that it displacements back to ambient do not exceed the travel for it.

Of course this damper will work only if the swing or movement is fast enough to engage the fluid in the damper.

Some other questions to explore are...
1)If the system has been in sevice previously and suddenly starts vibrating why the sudden change?

2)If it is flow induced vibration can the system be redesigned to eliminate the vibration?