Exactly. You could forgo the solar power altogether and run the thing off of a small battery system, say 4, 12v golf cart type and a tiny generator. A Honda EU1000 would probably do it, but an EU2000 would for sure and last longer - coupled with a 15-18 amp 48v golf cart battery charger. This would allow you to run your ac from a single EU2000 generator saving about 1/2 the fuel of your roof mounted AC unit and a 3000W or larger (plus twice the cost and weight) genny. This would allow you 5+ hours of AC run time in the evening, after generator hours have ended, on those occasions when it is still hot or just to remove some unwelcome humidity. I'm sure if you are just trying to cool your bedroom and it's not too hot outside the variable speed compressor would scale back quite a bit extending your cooling hours even more without getting a crazy big battery bank.
Or you could make a hybrid system using say 3-500 watts of solar, a small battery bank and a small generator. Lots of possibilities for off grid AC when your power requirements are so low.
"There is no worse tyranny than to force a man to pay for what he does not want merely because you think it would be good for him." – Robert Heinlein