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When you get a black screen in MultiMAN or any other Backup Manager it's normally to do with a modified EBOOT but sometimes you can get it working if you fix SFO files to do that just load up Rogero Manager and press L1 + Start it may ask you if you want to delete the game from your internal HDD so be careful but if you press no to that then the fix for the SFO files will come up.
If it is the EBOOT though just search Google: Original Modern Warfare 2 EBOOT.BIN then FTP the file over.
I hope this has helped.
try putting the game on ext hard drive then trying the select and x from multiman
The select+x method with MultiMan ONLY WORKS FROM EXTERNAL HARD DRIVES. The method bypasses the payloads which happen to take up the memory allocations that these black screen games need access to. It basically direct boots it off the external drive, using a dynamic on-the-fly file redirection. Pretty ingenious design from what I've read about it. I don't know why no one else mentioned that, and I'm only here instead of the general and jailbreak sections cause I'm really bored today, so it's a fluke. That game is only confirmed to be working on MultiMan, only when select+x booted, and only from external.