Question: I would like to do something like play.clubpenguin.com. 

What it does is that, when you visit the site, maybe using firefox or IE, if you opened a new tab or use other browser, when you visit that site again, it will show something like: "Please close the other browser that opened this page" or something like that. 

How to do this? (Its client's request)

More information: The site is Flash site

EDIT: 

Ok, i think this is a tough question, well, in general, Can this be done using php, mysql and JS?

Answer: 
A few options spring to mind...

1. When they first open the site, you'd need to store the user's current state in a cookie or similar, which you'd check for every time you open the site. If the state is Active, then it means they have another window open. The problem in ensuring that the state is cleared when they leave the original site window - you'd need to listen for the `window.onunload` event, and clear the state at that point - but you can't 100% guarantee this will happen.
2. Otherwise, you could place a script on the site which pings a server script every *n* seconds, notifying the server there is a window open for that client, and prevent new windows being opened until there is a lapse in pings.
3. To get more complex, you could maintain a persistent connection between the server and client (via sockets or similar), which would keep note of the same. Less calls from the client, a bit more complex to set up. See <http://www.kirupa.com/developer/flash8/php5sockets_flash8.htm> for basic info on flash + sockets.
4. Given you're working with Flash, you could look into Local Shared Objects (flash cookies) to store the state. Still possible to miss the unload event, but at least the cookie is persisted across all browser sessions and browser types.

Option 3 is the best IMHO.
Solution:

Response your clients request with a NO, because you are the webdesign guru that knows what's the best for the client's visitors. the website doens't have to appeal to your client but the client's visitors. and when they are limited so hard on their own computers they are everything but satisfied.