You can't do full-software PS2 emulation on the PS3. The GPU architectures are too different, and the PS3 is not powerful enough to emulate it by brute-force in software, like you might be able to do on a powerful enough PC.
The first-gen PS3 had full PS2 hardware inside, both the PS2 CPU and GPU, so it was very easy for it to run PS2 games.
To save money, they removed the PS2 CPU hardware in the 2nd-gen PS3 but kept the PS2 GPU hardware, and emulated the PS2 CPU in software.
In the current 3rd-gen PS3 systems all of the PS2 hardware has been removed. The PS2 GPU was the main requirement for emulation, so once that hardware is gone you're never getting the PS2 compatibility back.