If you want diversity and fairness, just play random civs and then switch your civ with your opponent in your 2nd game.
For example, if in the 1st game you got turks vs koreans by enabling random civs, then you can play koreans vs turks in the 2nd game. If it's BO3, BO5 or BO7, then you and your opponent should keep picking random civs and switching with each other until the last game, the most decisive one.
Problem solved ;P
For example, if in the 1st game you got turks vs koreans by enabling random civs, then you can play koreans vs turks in the 2nd game. If it's BO3, BO5 or BO7, then you and your opponent should keep picking random civs and switching with each other until the last game, the most decisive one.
Problem solved ;P