In single player there's not much. Soldiers are supposed to shoot, not talk.
As far as I can remember the story there's a bit of swearing on the radio throughout the whole mission, but a lot less than 3-4 times per level. There are plenty of levels with normal mission briefings and instructions and without any bad language.
However, you'll probably have to stay away from multiplayer games, unless you disable voice and text chats. People in CoD are no soldiers. They love trash talk in MP games and muting them completely is probably the best idea. (In CoD, I have voice chats muted at all times, although I don't care about language. Listening to those guys is just a real pain.) Also cheaters are usually getting insulted. And there are a lot of them.
To mute voice chat:
Multiplayer > Options > Voice Volume set this to 0
To disable text chat: put
cg_chattime 0 in your config located at
$:\path-to-steam\steamapps\common\call of duty modern warfare 2\players\config_mp.cfg
Enjoy CoD free of swearing.