You need to go to a battery store, and not just a Wal Mart or local Tractor Supply. Here is the parts breakdown, but Cub Cadet lists the battery as no longer available
There should be a common made automotive 12v battery that will fit in the tractor, but it is NOT a lawn and garden tractor. Take the measurements of the battery tray to a battery store and they will tell you all of the sizes of batteries that can fit.
You can look up the manual on MTD's or Cub Cadet's website, with the serial number and model number off of the frame. The diesel Cub Cadets used a standard automotive battery rather than a lawn and garden battery, and that's where the cranking amps come from. It is also a different battery than was offered in standard Cub Cadet tractors, so a manual from another (non diesel) cub cadet will not help you.
Also, you should check the manual to see how to operate the glow plugs. I believe that you need to turn the key to the left, hold it a few seconds, with your thumb over the round opening (#8 on the following diagram) until your thumb is warm before starting. This makes all the difference in the world when starting a diesel.