I spent almost an hour trying to figure out how to swap PSX discs, but thanks to a youtube video I was able to do it. I decided to write a tutorial in hopes that it gets added to whatever help/faq bizhawk has since it's not really very user friendly.
Step 1
For multidisc games, you need to make a .m3u file. It's really simple:
-Make a new notepad text file (.txt extension)
-Paste inside the filename of the .cue for each disc. For example:
Final Fantasy 7 (disc1).cue
Final Fantasy 7 (disc2).cue
Final Fantasy 7 (disc3).cue
-Save and close the text file. Now, name the file whatever you want, but make sure to rename the .txt extension to .m3u, and that will be all.
Step 2
-Now, open Bizhawk, and instead of loading the individual disc .cue, just load the .m3u file.
-Once the game prompts you to change the disc, go to PSX -> Disc Controls. On that window, you'll see all the discs you added to that .m3u file you created. Go on and hit "Open" on the "Tray" option.
-Now this is where it might get tricky for some. Bizhawk automatically pauses the game when the screen loses focus, so you either need to hit the Frame Advance key (Config -> Hotkeys -> Frame Advance) or you need to disable the auto-pausing feature (Config -> Customize -> Run in Background). Once you have advanced at least one frame, or if the emulator is not paused, then you'll be able to pick the disc you need from the Disc Control window. So, pick the disc and hit "Close" on the "Tray" option. When you go back to the game, the new disc will load.
Or you can just watch the youtube video I used:
https://www.youtube.com/watch?v=lWNc38QH5LY