PS2's actually run at 12V DC internally. So what you'd be doing is taking a 12V DC (average, it does vary) supply, using an inverter to convert it to AC, then converting it back to 12V DC. pretty silly if you ask me... and very inefficient.
Its pretty easy to build a voltage stabiliser out of mobile phone chargers that plug into cigarette lighter sockets. gives you a nice clean 12V DC supply, which you can then wire into the PS2, bypassing the internal converter. Total cost would be about $20 max plus some soldering time.
Or if you have a slimline PS2, you can buy car power supply packs for em premade.