Does the 2960 support tftp when it rommon mode? Can you set a 2960 to download it's image from a tftp server? If not is there any other way to get he bin file on the switch without waiting for xmodem?
not possible by tftp you need to download image via xmodem if switch has corrupted image or deleted image.
switch: copy xmodem: flash:image_filename.bin
Go over this link - using xmodem
Unfortunately TFTP is not supported in rommon on the 2960 switch. You will have to use xmodem to load an IOS to the switch. There is a much faster way to upload the IOS. It will take minutes instead of hours.