Unfortunately, CS4 is not fully "Cocoa" so it tends to be unstable on 10.6.
I wouldn't say that not being Cocoa leads to more instability on Snow Leopard, but certainly CS5 which is Cocoa performs better than CS4. If CS4 is not stable (meaning crashing a lot) I suspect other things are at the root. Disabling Open GL in Photoshop CS4 can help. Also be sure that all the CS4 components are the most updated.
The most common problems that cause crashes are really due to either bad hardware or faulty OS and application installs. While it's painful and time consuming to do, I would suggest considering a complete backup, wiping the drive and doing fresh installs of the OS and CS4. I suggest that really as a last resort and not something to be done lightly, but if your system and applications are having problems, it's the best way to get to an known optimal state.