I know for sure that Black Ops 2 is very buggy with LAN and errors like this...you could get everyone to delete the updates for Black Ops 2 then try and connect over the network...one person might have to be signed in to an account then the rest can play...if the games were updated over a bad connection the updates could be corrupted...when i updated over a certain 3g connection updates would always be corrupted.
Well i guess make sure that the settings for your router allow for connection sharing...have you tried other multiplayer LAN games?...
But practice with at least one other ps3...maybe both delete the game data and try to connect.
Looks like they just sent out a patch to fix yer problems...;
Multiplayer Issues Addressed
Resolved an issue where players were receiving an error message when trying to join a System Link or LAN Party lobby without internet connection.