Quoted:
Just did a quick search online, a small (8k btu) window air conditioner needs 815 watts for operation (and presumably more for startup).
To run that for just 12 hours a day you would need solar panels with at least two to three times that capacity feeding into some deep cycle batteries.......
You could do it yourself for less but if you bought an off the shelf 3kw kit online it would cost you around $15k.
Good summary by MarkNH.
Details, so I don't feel like a looked this up for nothing:
Installed 2kw home system: About $16,000, very close to MarkNH's number. http://www.solarbuzz.com/solarindices.htm
A 1000 watt medium window unit, running 14 hours a day, uses 14 kw-hrs of energy per day.
Assume your cost is 15 cents per kw-hr (a little above national average).
You'll use $65 of energy per month, or $391 per year (running the unit 6 months per year)
Over 10 years, you'll spend $3910 to run that window unit.
So, $3910 over 10 years for no solar, vs. $16,000 with a solar system. After 10 years you'll be looking to do some serious maintainance on your batteries, but probably not a full replacement cost. Maybe another $5,000?
So, no, not even close. Unless you start scrounging for used batteries, panels, and can build up your own storage and inverter control system.