I don't have a PS2 adaptor yet myself, but I seriously doubt it supports wireless capablities on its own. There may be something avalible to allow this, but I am not 100% on that. Your best bet would be to by a ethernet wire and hook it up to your router that way. Sure it would be a pain to have a wire laying across wherever, but you can always unplug it when you're done.
Or if thats undoable you can try searching google to see if there is infact something to let your PS2 work with your wireless connection.
EDIT: Yup, I was right, you need some extra hardware for the PS2 to work with your wireless connection. I just pulled this off of the ps2 offical site:
"There are also wireless solutions, but these require the purchase and use of additional networking hardware..."
http://www.us.playstation.com/peripherals.aspx?id=SCPH-10281

Your laptop wouldn't really come into play in setting up a wireless Playstation 2 connection however you are going to need more equipment.
You already have the first step with your wireless router. The second thing you''ll need is a Network Adaptor for your Playstation 2. You can pick those up at any E.B. Games or Game Stop location. Here is what they look like:
E.B. Games: Playstation 2 Network Adaptor
The final thing you'll need is a wireless bridge that will connect to your PS2's Network Adaptor and receive the signal from your wireless router. You can find those at most computer stores or online. Here is what they look like:
Wirelss Ethernet Bridge
However you may run into some connection problems depending on where the wireless signal has to travel through your house. If you find this is a problem then you could always go with a Cat 6 cable. That would mean your connection is wired instead of wireless but the signal will always be strong and it's a little less expensive.
Most importantly be sure to shop around before you buy any equipment. You can usually find better deals that way.
Hope this helps!

It is very possible and quite cheap. You will need a LAN port to connect a crossover cat-5 ethernet cable. IT MUST BE A CROSSOVER cat-5 cable. You can find it at any local computer store, and it will be clearly labled as crossover. Simply plug it into ps2 to the the laptop. I assume you're running WinXP. After you have the cable connected, go into your Network connections. You should see the wireless connection icon, right click it, and scroll to "share this connection". Now you can use your wireless laptop for a Net connection for your PS2. However, when the ps2 is signed in, the laptop must be on.

I was able to hook my cube up to my wireless laptop... it lagged on Mario Kart, but still ended up working. If I have to buy additional stuff, I won't do it. I can already play online on the family TV... but can only do that late at night when no one is watching TV.
reign: I think I tried doing that already, or maybe I did something close to it. I already have a cross over cable... I'll have to try it again. And do I just insert the cross over cable into laptop and ps2, do "share connections", turn ps2 on... and then thats it? Or is there more to it? (like doing anything to my wireless router settings). Thanks.

You shouldn't have to open any ports. You've got it, Simply do the steps you've just listed. This is how I connect to XBL. Just curious, what router/wireless set-up do you have..as far as company?

A linksys.

sweet, it worked... thank you. Only prob, it obviously lags more than if I was on my other tv... but once I turn off every comp using this wireless connection, it runs good.

Congrats. Obviously a wireless connection will not be as strong as a hardwired one. But also depending on which Linksys router you have, your connection could improve greatly (wireless B 11Mbps, as opposed to wireless G's 54Mbps) Though it may lag from time to time, it's definatly playable, and a lot cheaper than buying a seperate adaptor.