Hmmm...sounds like a serious TV problem there.
As far as I know you can go down to Radio Shack or somewhere and purchase a "game adapter" that will convert the video RCA signal into a standard RF cable input (most of these come with a switch to allow you to go between the game input and regular antenna). The only problem I can see is what to do with the audio signal from the PS2. Maybe you could find another coverter that would handle all three RCAs, or at least video and mono audio.
I\'ve also got one of those TV\'s with the built-in VCR. Tried to use it while on vacation to "take my PS2 on the road."
Unfortunately, because of the VCR, it refused to accept the PS2 signal at all. Really sux.
Good luck!