I had a look at the different leader boards for the game types and had a look at how much score per minute each game type was earning the player at position 1000. The highest score per minute was Hardpoint at around 575 score per minute. A close contender was Headquarters with around 470 score per minute.
At the end of this guide there is a YouTube video with a visual version of this guide.
Other game types that are very close to Headquarters in score per minute are Free for All, Demolition and Domination. Kill Confirmed also isn’t bad. The other game types have very low score per minute (Team Deathmatch had around 300 score per minute).
The other thing you can do to rank up faster in Black Ops 2 is to use the each weapon only until you have ranked it up fully. Each rank you get unlocks different attachments which in turn grants you some experience. Also when you complete camo challenges (which are to get specific number of headshots with each weapon) you gain some extra experience. Each game type has challenges associated with it as well as each score streak, so vary up what you play and what score streaks you use and you will rank up much faster.