This thread was able to help me fix the server unavailable error. Just followed the directions and it worked instantly. It seems that it basically has to do with WHEN you sign into psn, you have to use the xmb and you have to start the game first. Follow these directions carefully.

STEP 1 - on the XMB menu delete the black ops 2 game data (not necessary to delete the save data)
STEP 2 - make sure you are signed out of psn
STEP 3 - start black ops 2 and update it (If prompted do NOT sign into psn)
STEP 4 - go onto Multiplayer or zombies (still signed out)
STEP 5 - finally sign on using the XMB menu NOT by clicking on “play online” STEP 6 - Then go down to options, while in the options menu press the select button to display system info. Current version should be (22.158.31.1458562) as of 11/20/2012 3:19pst. Finally exit options menu and select “Play Online”, if this fix worked you should be connecting and no longer receiving errors.

Credit for the original post on nextgenupdate.com to oViiPeRx

This method doesn’t work for everyone, but it did work for me and a lot of other people as well. After days of getting this error, it is worth trying.

The reason viewing the current version is important is because for most people receiving the server error, the version was stuck on 20.0.-1 and would not update to the current hotfix version.

GOOD LUCK