first, yes you can download "codes" from other users. Have you used NeoEdit yet (is that the program you refer too)? If so, it is as simple as downloading another user's configuration (ncf file) and copying buttons/pages etc into your own ncf (open both your and their ncf and cut and paste). That is the easiest way. You can still use your own buttons/designs, just copy someone else's button with the codes already intact and change the button's appearance once it is in your ncf. If you are having trouble with neoedit make sure you have the latest firmware installed on your neo and that you have the latest version of the neoedit software.
The other way to "copy" codes is a bit more involved. You'd need a program called neohacker and you have to go into another user's ncf and cut and paste the actual codes into your own ncf. I wouldn't recommend this for something that is as simple as this.
Second, I would bet a gazillion space bucks that Sony uses the same codes for PS2 that they do for the slim PS2 and probably will use them again for PS3! Find a user whose ncf has the PS2 device codes and copy that device to your ncf. try it out and see if they work.