There are many websites which claim to offer serial numbers for Zoo Tycoon 2. In my experience, however, it's unlikely that any of these will actually work. I'll explain why in more detail below...
Why are serial number websites of little use?
Serial numbers are a way of confirming that a user has user has purchased a game, and each serial number is therefore unique to each purchased game.
For the most part, people will have already used their personal serial number following their purchase of the game, and therefore, there are unlikely to be many valid serial numbers in circulation.
What are the options?
As mentioned earlier, there are numerous websites which claim to provide serial numbers for Zoo Tycoon 2. You could take a risk and try one of these websites, and you may be lucky enough to find a valid serial number, but it's more likely that you'll be disappointed.
Another option would be to attempt to download a valid serial number from a torrent website, but again most of these will have already been claimed. I would recommend that you simply buy Zoo Tycoon 2, and use an authentic serial number, which is of course the only legal option.