Is the convenience module the door lock module that controlls the central locking and puddle lights??
I only ask as i need a drivers side one as my central locking from key fob doesnt work lol.
Just to butt in here - when I bought my Mk4 a couple of months ago the central locking didn't work from the key fob. After a bit of reading, I discovered the following which worked for me:
- Disconnect the battery negative terminal and leave unplugged for 10 minutes (make sure you note down any radio codes etc, before doing this)
Re-connect battery negative terminal
Voila - you've got remote central locking again 
Not necessarily going to work for everyone, but with mine I could lock and unlock the drivers door, but not any of the others (you obviously need to press the key fob twice to unlock all other doors, but even this didn't work). Now it works fine, simply after disconnecting the battery - I believe it resets the convenience module (or maybe something else, I'm not sure).