More than likely it's your laser getting out of alignment. I've fixed 5 or 6 PS2's in the past when they had the infamous "disc read error". But first, and the easiest step would be to open your unit, use a q-tip and alcohol. Rub lightly on the lens when cleaning as not to scratch it. I'm not sure of the glass hardness or any coatings on the lens, so I'm not sure how easily they can be scratched. BTW, the alcohol not only helps the Q-tip absorb dust, etc, but dries and disvoles any greasy film on the lens.
As for disc cleaners, I've used the Game Dr. scratch remover and a memorex cleaner/scratch remover. The Game Dr. works about 10 times better. Don't get the hand crank model unless you like making homemade butter/icecream. Some have power adapters included and some don't. Don't get screwed with the unit that doesn't have the power adapter included unless you like purchasing batteries every week. The Game Dr. has fixed about 95% of my games that were previously unplayable.
Last but not least, google "PS2 repair" "disc read error", because most likely your problem is realignment and it's a very easy procedure to repair. Good Luck W.