I try to open a game file and it tells me that it cannot run BIOs files. I have all of the BIOs files available, but for some reason it doesn't work. The game is Japanese, if that is an issue (I have the Japanese BIOs, though.) Any suggestions?

Did you put the BIOS files in the correct location?
~/Library/Application Support/PCSX/Bios

Yes. I'm not sure what type of file format PCSX runs off of, though and it wasn't easy to find on Google. I have a bin file and when I unarchive it, it makes it a .bin.xxxx (can't remember name now). What is the file extension used by the application?

.bin