Hi,
If you wish to reliably run the air conditioner there are several choices. Here they are in ascending order of price.
A. buy a 3000 watt Yamaha sIEB (b is for boost) generator
B. buy a pair of 2000 watt generators with a parallel kit
C. buy a single 2000 watt generator and a hybrid inverter such as the Magnum 3012 or a Victron.
D. Put 1250 watts of solar panels on the roof, add a large battery bank, and add a great inverter such as the Xantrex pro watt 2000 watt inverter.
I have chose A. I will shortly be able to do C. Next year I hope to do D.