May not be an option for some (don't like change?), but I find switching to Tactical helps alleviate that issue. Knifing is not a big deal in MW3 as it was in other games. Less lunge forwards, prevents your weapons from gaining XP if you knife (tac knife excluded maybe?). Also, playing Battlefield may have skewed my perspective as it by default uses R3 to crouch and Circle to knife.
I find in CoD games I knife a LOT accidentally, causing a premature death, but after switching to Tactical (only swaps R3 and Circle commands) and adjusting your Ragnarok controller thusly, it helps a LOT. It may take some getting used to if you knife a lot though.