I own a Honda 2000. It is very quiet, and it is a great generator. If you hunt around, you should be able to pick one up for under $900. We had some success with using the generator to run the 13Kbtu AC on our previous trailer, but only after adding a hard start capacitor. I don't recommend that setup, if you want to rely on having an AC. It would start most of the time, but would sometimes not restart after the compressor cycled off and then on again. Also, the quietness of the Honda 2000 was no longer there with that high load, and the gas runs out pretty quickly at that load. We still love the Honda 2000 for other generator needs, but as an AC power supply, it didn't really cut it (and doesn't work at all, now that we have a bigger trailer with a 15Kbtu AC).
We looked at the Yamaha 2400s. Also a nice generator, but they were too bulky and heavy. The Honda 3000 is great (not the new 'handi' model though - that one is loud). But, the Honda 3000 is not portable by any reasonable stretch of the imagination.
If I were to decide that a reliable generator source for an AC was necessary, I would buy a second Honda 2000 (the new Honda 2000 companion, with an RV plug) and run them in parallel. Having a second Honda 2000 would allow me to bring just the one Honda 2000 for times when I didn't need AC. Or, if I needed AC, lifiting two Honda 2000's separately is much easier than one Honda 3000. If (like me) you are not sure you really need a quiet generator that runs the AC, but do want a generator for other things, the Honda 2000 provides a great upgrade path later on, if needed.
By the way - I also own a Champion 3500 generator, which runs the AC fine. So far, the only times where I have wanted AC and didn't have hookups were trips where the noise level was not an issue. At $300 (on sale), that is an inexpensive solution that works for many.