Run the AC Off Battery — Kit
The usual answer to air conditioning off-grid is a rooftop unit and a 3,000W inverter with a battery bank to match, which is a five-figure conversation. The other answer is a low-draw portable unit and a station big enough to carry it: the Cybertake S2 Pro pulls a fraction of a rooftop Penguin, and the AC200P L has the rated output and the capacity to run it through a night at a sensible setting.
The parts in the one-click kit lead this list, followed by the other sizes and brands that do the same job, so you can swap a part before you buy. The whole kit, priced and loaded in one click, is on the RV power bundles page.
How long will it run? The free RV Solar & Battery Calculator includes the portable 12V AC and shows the battery and solar you need for the hours you run it and the overnight temperature.