Lippert should be able to tell you the pinbox model if you give them the serial number. If not, measure it. Then, go to http://www.pullrite.com/pdfs/QCCP.pdf
where you will find the numbers which will tell you the model.
Note: Even though I linked to a Pullrite page, the numbers are universal.
Having said all of that, are you sure the bouncing is something which can/will be corrected with a different pin box? When you say it bounces, what do you mean? Are you experiencing "chucking" which moves your head front to back each time your truck goes over an expansion joint or are you experiencing something different? Can you describe the motion you're getting? For example, you might be able to cure the problem with air bags on the truck or Timbrins http://www.timbren.com/
which are considerably less expensive.
You might be able to correct the problem without going to a new box and save money at the same time. If the problem is in the truck suspension, for example, a new pin box won't solve anything except for that excess bulge in your left rear pocket.
Edited by: jeb