Create a virtual memory card first
Turn on your PS3.
Select “Memory Card Utility (PS/PS2)” under the “Games” menu in the Cross Media Bar.
Click on “New Internal Memory Card.”
Select either “Internal Memory Card (PS)” or “Internal Memory Card (PS2).” The PS memory card will allow you to save data from original PlayStation games. The PS2 memory card will allow you to save data from PlayStation 2 games. Depending on what types of older games you want to play and save, you may need to create one of each.
Rename the memory card slot if you wish. It is recommended that you leave in either PS or PS2 to denote which games are able to save in that slot.
Assign the memory card to a slot. If you have not created a memory card before, you will be prompted to assign it to Slot 1. Multiple memory cards will be assigned to Slot 2 and so forth. Some PlayStation and PlayStation 2 games require the memory card to be assigned to Slot 1 in order to read properly. You can change the assigned slot at any time.
It's been awhile since I played a PS1 or PS2 game on my PS3.
If I remember correctly, you need to set up a "Memory Card" in your XMB.
Under "Game > Memory Card something something"
You can create virtual PS1 and PS2 Memory cards.
Hope this guides you on the right path.
Why the double post?
Because by the time I finished trying to write and post my response, the member above me had already copy / pasted one.
I don't intentionally repeat post on threads that already have a definitive solution.