Real world experience, for what it's worth...
I had (and recently sold) a 6x10 heavily insulated (that matters, a lot) cargo trailer with 600 watts of panels, 7200 watt-hours of lead-acid golf cart batteries, and a 5000 btu air conditioner. These were enough batteries if fully charged to easily run the AC overnight and more, and enough panels to about break even (or usually a little better) running the air conditioner and little else all day in high-intensity-sunshine Florida. Note that the panels would _not_ both run the air conditioner and fully recharge the batteries-- only the fact that I traveled often during daylight (which allowed recharging on the move with the AC not running) made this system work so well for me. (Plus, I was willing to run a small generator as needed to top things off. This almost never happened in actual practice.) My guess is that this would _not_ be enough of a setup to satisfactorily run an AC unit 24/7 for most full-time folks, who don't move around as often as a pleasure traveler. (Though it's getting close.) In practice I started all my trips with a full charge, then usually got 2-3 days air-conditioning off of solar alone if I was willing to let my batteries run slowly down to 30% or so-- which I was, because I'm not a full-timer and this therefore didn't happen often enough to significantly shorten the life of the batteries. By then I'd be ready to move again anyway, and the batteries would recover as I did so. For someone with my specific, exact needs this setup was nearly ideal in terms of cost/benefit ratio. Besides, I didn't have enough roof-space for more than 600 watts anyway.
If I remember correctly Jim In Denver (who I consider to be an extremely knowledgeable and reputable source of information-- he helped me a lot and I remain grateful) once suggested about 1200 watts as being roughly what's needed to support a small window AC unit full time. I also have a 1200 watt off-grid system on my home-base mobile home, and having operated it for a couple years now I tend to agree with him. This is my backup power source for hurricanes, and is specifically meant to power a small air conditioner to cool a single room (plus a laptop and an LED light or two) if and when required, for as long as required. At least in Florida, 1200 watts of panels is indeed about right for this, leaving an adequate cushion for cloudier days. (Even with 1200 watts, two or three _extremely_ cloudy days in a row means getting out the generator.) If I mount a solar system on my newer, larger cargo trailer-- I'm still working out the cost-benefit analysis-- it'll be about that same size or, if possible, a little larger. As for batteries... At the time I built that 600 watt system, LiFePO4's were (for me) completely unaffordable. Today I'd wait for Black Friday-- when last year at least the sales were huge-- and spring for three quality 1200 watt-hour units instead. The weight and efficiency gains (I went to 6000 watt-hours of lithium on my home system last November) are IMO well worth the extra cost at Black Friday prices. If you can't wait until then, I'd go with the same six golf cart batteries I used in my original setup. They served me well.
Best of luck! For me, the solar turned out to be more fun than the rest of the build combined, and it'll probably be the same story on my newer trailer when the time comes. Making my own electricity has become my major hobby.