Basically, a 3,000 watt generator is the minimum size. Some folks report getting the Yamaha ef2400is to run an A/C but it seems to me that it might be rather low on the current.
I have had fine performance with (2) 2,000 watt generators with a parallel kit, yielding 3,000 watts. The A/C starts just fine and runs without issue. There is not a significant drop in the voltage that I have yet measured. Using a pair of generators allows me to use one relatively light-weight generator when I only need to recharge a battery, or both if the A/C is needed but still not having to individually lift a heavy generator.