I hate to say this, but your PS2 has aged to the point where the drive is wearing out. I suggest you try to clean it though. I've done it several times, and it usually works like new afterward.
Here are the (rather non-specific) instructions:
1. Remove the cover of your PS2, so that the drive is clearly visible.
2. Carefully remove the cover on the drive, exposing the tray and laser.
3. Take a soft Q-tip, dipped in the purest cleaning alcohol available, and clean the laser "eye" until it is completely clear.
4. Put the drive together carefully, and clean any remaining dust from the console before putting everything together.
I hope this helps, my friend. Keep the 2's alive.