here’s a thread from the tiny teardrop trailer forum that I stumbled on a few weeks ago re: running an AC off battery overnight.
http://tnttt.com/viewtopic.php?f=21&t=66150&sid=1042cc9fc9833f03a0e1b361b8b64a2f
the person who posted it calculates that it can be done. he plans to use a 5000 btu AC which I agree with restonthewind would be much larger than needed, but maybe a smaller one can’t be found.
the spec sheet for this 2500 btu ducted unit:
says the power draw when cooling is 480 watts. so this is twice the power consumption that the author of the post I linked to assumed ( he assumed 500watts for 5000btu/hr) so 2500 btu/hr might deplete the battery overnight. you could always wire two deep-cycle batteries in parallel which would double the available power, and still be at 12volts.