The first thing I'd try would be a new adapter and / or coax cable. Sounds like one of them may be fualty.
If that doesn't fix it, you could try picking up something called an RF Modulator, they have them at Radio Shack. Usually about $10. It basically lets you plug various things into it, then it routs them through a single coax cable that you plug into the TV. So you'd plug the yellow, red and white cables from the PS2 into it, and also the coax cable from the wall / cable box. Then you run a single coax cable from the RF Modulator into the TV.
Here's one from Amazon:http://www.amazon.com/Audiovox-Corporation-CRF907-RCA-Modulator/dp/B0014KKV7W/ref=sr_1_1?ie=UTF8&qid=1328220271&sr=8-1