Redsaber:
Technically, you CAN have such a script. It's just basic math, which JavaScript can do. The core issue though, is to KNOW a particular person's date of birth. How do you plan on storing that? Where? You have to store it somewhere that is accesible by your code.
If by "your code" we mean "code residing on and processed by your web server", then you would store everyone's birthdays on the server. You'd either use a database, such as MySQL, or an XML file.
If by "your code" we mean, JavaScript running on the browser, then you're faced with that fact that the birthday will have to be stored on the individual user's machine. The only way to do that is via a cookie.
The problem with that is, cookies don't last. The user can decide whether or not to accept cookies in the first place, and can arbitrarily delete them. For example, on my systems, the cookies don't last beyond the current browser session. So you could "remember" my date of birth for about 5 minutes, which renders your script useless.
That's why, in my opinion, my first answer is correct: "No.", there isn't a simple script to do this, and you'll need server-side code coupled with a persistent data store.
In that script you referenced, notice that a date is being passed into the "countup" function. You have to ask yourself, where did that date come from? It's hard-coded in the …