Without knowing what AC unit we are discussing nor how much you use it each day, I found the specs for a Coleman 9200 BTU (

http://www.campingworld.com/shopping/item/coleman-mach-8-cub-air-conditioner-arctic-white-shroud/72717). It specs 1550 watts while running at 100 degrees outside temp. I have no idea if it cycles (duty cycle) or how much power it consumes on average so all of this is just a guess based on very little information. The actual measured power consumption from your AC unit would make a big difference.

1550 watts = 124 amps DC (1550/12.5 volts)

Run AC 8 hours

8 hours x 124 amps DC = 992 Ah/day DC

If you had a typical lead-acid battery bank, you would need a 2000 Ah bank to run the AC for the 8 hours (to avoid going below 50 percent state of charge). Assuming 230 Ah 6 volt GC2 batteries, you would need twenty of them. This would weigh something around 1600 pounds.

You would need at least a 2000 watt inverter to run your 1500 watt load. However; that is cutting it close (startup load and all that) so something a little larger is probably a better bet (like 2500 watt).

I have no experience with the things that smooth/handle the startup voltage so can't answer that.

You would then need to replace the 1000 Ah of power used from the battery bank each day, that is 12,500 watts. Assuming 6 hours of good sun, you would need 2000 watts of solar (12,500 watts / 6 hours). Using the large, higher voltage, residential panels rated something around 400 watts, you would need five of them. You would need an MPPT solar charge controller that can handle that kind of power - probably two or three networked together.

I have no knowledge of such large systems but I do know that Lithium batteries would offer a DISTINCT advantage in this scenario (size, weight, and storage capacity) as would a higher voltage battery bank (say 48 volt).

A generator to run a 1550 watt load would be a 1550 watt generator. However; the startup load has to be considered so possibly more like a 2000 or 2500 watt generator.

Edit: Peukert's law probably throws all the above calculations out the window. I'm not sure if pulling a constant 125 amps out of a bank of twenty batteries would be an issue or not. All just theoretical, for the fun of it!!