The device manager of 2960 switches come inbuilt with the IOS used. But the IOS filenames should end with ".tar" rather than ".bin". The size of IOS tar files will be more than IOS bin files.
IOS with Web based device managers
c2960-lanbasek9-tar.122-35.SE1.tar
c2960-lanbase-tar.122-35.SE1.tar
IOS without device managers
c2960-lanbase-mz.122-35.SE1.bin
c2960-lanbasek9-mz.122-35.SE1.bin