At which point does the game ask for one? Perplexed by this, I just tried to join an online multiplayer game, and it joined without any problems.
The game card thing doesn't mention a need for cd-key either.
So my suggestion is to either give more information, or if you haven't already, check the game to see if you even need one.
/edit: I did some digging and found out that every GOG copy comes with the same CD key or something. Dunno how much that affects stuff, but I can now see why you want a unique one. As I'm uncertain whether you already used this
http://www.gog.com/en/support/contact/technical_issues_with_games for the cd key request (or just sent emails), I'd suggest sending a request through there. Just pick your game title and "I have a problem with: multiplayer key request". Then write that you want a unique one. It might take a few days (you didn't mention how long you have waited, and it's hard to tell what others consider "any effort").