I've been searching around and the best way to play backed up CDs and DVDs Is this.
First you Have to have and know some things to continue and succed You Need:swap magic CD v3.0 & DVD v2.0
gameshark version 3/4
cdloader v7 & adobe reader 3.0+for PDFs
you can download cdloader from the internet (search in google)but the gameshark and swapmagic you have to buy because there coded for PS2. Finally you need to find out what version PS2 you have if you don't know, you can go to http://www.mod-chip.com/ps2version.htm Ok once you've done all of the above you can follow the directions below and play PS2 backup games. ENJOY
Gameshark 2 V3/4/AR MAX
CD BACKUPS
1. Insert and let gameshark V3/4 boot
2. Select the codes you want/if none skip this step
3. Select Start Game
4. The cd/dvd drive will now eject automatically.
5. Replace the Gameshark 2 V3/4 with the swap magic cd.
Once you have made the appropriate swap press eject to close the cd/dvd drive and press x.
6. Once the Swap magic cd has loaded do the following...
7. Swap the swap magic cd with the cdloader using fliptop/knife trick and press x.
8. Once the cdloader has loaded press eject and swap the cdloader with the swap magic cd and press eject to close.
9. Wait about 7 seconds and swap the swap magic cd with your cd-r backup and press x.
10. Your backup will now load with cheats.
DVD BACKUPS
1. Boot Gameshark 2 V3/4
2. Select the codes you want/if none skip this step
3. Select Start Game
4. The cd/dvd drive will now eject automatically.
5. Replace the Gameshark 2 V3/4 with the swap magic cd.
6. Once you have made the appropriate swap press eject to close the cd/dvd drive and press x.
7. Once the Swap magic cd has loaded do the following...
8. Swap the swap magic cd with the cdloader using fliptop/knife trick and press x.
9. Once the cdloader has loaded press eject and swap the cdloader with a high toc original such as the swap magic dvd and press eject to close.
10. Wait about 7 seconds and press x.
11. Once the screen that says "swap dvdr by ea method" comes up swap the high toc original(swap magic DVD) with your dvd-r backup using fliptop/knife trick and press x.
12. Your backup will now load with cheats.
notes:In step 7 in CD backups and 8 in DVD backups, if you have a version 9/10 and not a version 1-8 swap the swap magic cd with the dvdloader not cdloader using fliptop/knife trick
and you can buy the fliptop cover for the PS2 it's not needed but quicker and easier then the knife/card trick.
The below link teaches you how to do the knife trick.