Plutonium

Found the solution:
First copy the game files out of the game folder (like copying all the files from the "Call of Duty Black Ops II" folder while keeping the folder there) to a new folder somewhere else. Then copy the plutonium.exe file into the game's folder. Rename it to whatever the multiplayer exe's name was. For BO2 you'd rename the file to "t6mp.exe." Then launch the game from Steam and it'll launch Plutonium. Select the folder where you copied the game files and it will work, recording your playtime.