I would look at 3KW minimum for A/C and the loads you can't really control unless you start switching off breakers, or pulling fuses to keep the 12V converter (needed for lighting and control of appliances) from trying to charge batteries. Yamaha makes a 2400 watt inverter genset that does pretty well starting an A/C when other loads are minimal, but smaller is going to depend on the details, which appliance models and combinations.
Manufacturer practice is to install minimum 3600/4000 genset with a 13,500 BTU A/C, 2400/3000 watt for a 9000/11,000 BTU unit.
When running off a genset, or even 30 amp shore power, beware of heating loads like coffee makers, toaster ovens, frying pans, griddles, blow dryers, vacuum cleaners. Any of these with the A/C running in a RV can take a 30!amp main over its limits. Blow dryers on high heat are sized to max out a 15 amp circuit, will be a problem for the main as well if running when an A/C tries to start. My daughters had to learn this the hard way, at the house as well as in the RV.
Also, if external inverter generators have an ECO (low RPM) mode, that will be a problem with air conditioners. Gensets handle surge loads by converting excess rotational energy into electrical energy, bogging down briefly to cover the surge. In ECO mode, the genset has to spool up to higher RPM as loads increase, and might not be able to do it for a good size surge. ECO modes are for light, no motor, loads that build slowly, not for motor starting surges.