Seriously, get a Honda copy 1-2KVA inverter generator. Don't fuck around with diesel gensets unless you need upwards of 10KVA.
Me personally, I run a dual battery with a 120 amp hour deep cycle battery as the auxiliary. Keeps my 110L Waeco running as a fridge for 3 days straight in 80 degree days. If I'm not moving for a week I'll start and idle for half an hour each day.
Just get an automatic isolator solenoid that connects both batteries once your main battery reaches a pre set voltage.