Either pay someone to install a chip in it, or do it yourself. Other options are swap discs with slide cards, but that is a really terrible solution. I think there exists softmods too now which is just a memory card with a special sort of program stored on it which will let you play unauthorized software (which a patched game is).

PS2 are made to only execute code that is authorized by Sony. That's why you can't just copy a game with your PC and expect it to work. Because you need to copy the game before you can apply the patch, you cannot get it to work without modifying your console to accept unauthorized programs.

Or, as I also mentioned: Use a PS2 emulator on your PC. You will need a 2.6 GHz intel CPU or better to be able to run most PS2 games through emulation without getting slowdowns within the game. You will also need a reasonably good graphics card.