That fastest I've leveled up in a single game was from 1-12 in MW3. The final prestige I stopped at I happened across a bad team who stuck around. I must of perfectly balanced my attack with various guns, equipment, and completed a bunch of challenges because the most I've ever leveled any other time was 8 levels.
The fastest I went from 1 to prestige was Black Ops II where I did so during a two day span of about 12 hours of gaming. Mind you, I played with a group of very supportive players. VSATs, EMPs, and nonstop airsupport was always up and we had strategies down to get the most XP. For a while there it was considered a bad game to score less than 5,000pts a game.
BO2. In 8 hours orso from level 1 to somewhere 30. Got a lot of weapons near gold that I had saved for after prestige.
One time in Gears of War 3, I leveled from 5 to 23 by having a monster game and completing craploads of challenges. It was spectacular.
In Cod, I'd say MW3 was the easiest to level up in, since you could go all the way to level 80. I don't remember specifics of what levels, but any given night, you could jump 30 levels in one solid night of gaming.
In MW3 the same game that I got my Mk14 gold I also got my Type25 gold and completed a DOM challenge. I think I walked away with somewhere around 50k xp because the DOM challenge alone was like 20k.
I dont know if this is fast or not, but its my fastest... i went through a whole prestige on Ghosts in 15 hours?
I did a prestige in BO2 in less than 8 hours by simply playing domination, rushing with EMPs, getting high kill counts and captures.