Currently (8th june 2022) working solution on Xbox: with the game closed, go to the console network settings and disconnect. Then start MW, a message warning you that internet is needed will pop-up, just press disconnect. Then start Local multiplayer and you will see clearly that they let you add the 2nd controller.

For Call of Duty: Modern Warfare 2 on the Xbox 360, a GameFAQs Q&A question titled "Will there be offline splitscreen, or Bots?".

The crossplay feature should be disabled from the in-game settings menu, according to several sources. On the console or PC, the split-screen problem is being experienced by numerous users. Reinstall COD Modern Warfare. Open Steam on your computer by launching it. Go to Library and then select Call of Duty: Modern Warfare with the right click.
Yes, split-screen is available in Modern Warfare 2 but only on console and your second player will need their own PlayStation or Xbox profile. Player two will also need an Activision
The answer is yes, you can play split screen in MW2 Multiplayer. However, as of this writing, not all modes will be available for play and it is only available on the PS4 and Xbox One. Split screen was missing from the Modern Warfare 2 beta, so it’s safe to assume it won’t be included in the new game as well. Unless Activision expressly Yes, actually, Modern Warfare 2 split-screen is available. It’s a bit of a surprise, since local co-op has been gradually removed from many multiplayer games over the last console generation . 282 351 597 744 666 747 904 499

is modern warfare 2 split screen