Diesel Generator Shuts Down When A/C turned off and on

How long are you waiting between turning the AC off and then on? If you don't let it sit for a couple minutes for the pressure in the system to equalize, it's trying to start the compressor against a pressure head and that's a significant extra load (both for the generator and the compressor motor).

Many thermostats have a time delay to prevent restarting the AC right after it's been turned off, for this very reason. Many others lack that nicety.