Since there is a very finite number of light-gun games for the PS2, you should be able to look at each of them. There's a notionally complete list on Wikipedia: List of light gun games#Sony PlayStation 2. The PS1 games should work, too.

That said, none of them appear to be railers, much less paintball-themed railers.

Edit: I take it back. Some of them are railers, but none are paintball.