We have two Honda EU2000i (one "standard" and one "companion", hooked in parallel); and Yamaha and other manufactures make fine, similarly-sized generators suitable for running your air conditioner.
Alternately, instead of two "2000" generators, a single "3000" generator (or larger) can be used. However, these models are much heavier, and smaller and/or older people may have difficulty moving/lifting them.
Make sure to check specifications for noise level, as even the quietest models aren't silent. Also, off-brands may be noisier and less reliable, with construction generators being the loudest.
Personally, I would not even consider using a construction generator; as you will make no friends in regular campgrounds. Of course, that's assuming they don't set fire to your generator, stone your Airstream, or run you out of the campground, tarred and feathered, on a rail.
Whatever generator(s) you select, all will use a lot of fuel while powering your air conditioner. So, if you plan to boondock and run your air conditioner 24/7, you should also look at "extended-run kits" that connect external fuel tanks to your generator(s). Please note that even with external tank(s) your generators will need frequent refilling, most likely every day.
There are lots of threads on this site that contain good information on generators. Suggest you use SEARCH function and do a little reading to see which brand and model will best fit your needs.
Here are a couple of links to get you started: