If it's happening only on FFIX (and it plays other PSX games without trouble) then I would guess that it's the disc that's damaged, and not the PS2.

If it doesn't play other PSX games then you might have a problem with the tray or laser alignment. In most PS2s (except for the really old ones; first two generations) it's quite easy to fix alignment errors. I've repaired several PS2s using the method in the guide posted by TSoL (and broken a couple ), but it really does work provided that laser alignment is the problem.

Putting tape or any foreign object on the disc causes it to be imbalanced when spinning inside the PS2, and this often causes the disc to jump off of the tray clip and ricochet around inside the PS2.

Personally, I'd just rip the game to my computer and play it through an emulator. You can use your PS2 controllers, and even use different shaders to "improve" the original graphics of the game.