Let's just throw out a few numbers here and see what we come up with. First, let's assume your air-conditioner is a 5000W unit running on 240VAC.
You really need a clamp meter for this, but the starting inrush power is likely to be 3-5X the running power. So, for the first 500 milliseconds or so, your inverter will need to supply somewhere between 15,000W and 25,000W to start it. There is no single inverter on the market that can do that. You would need at least two LARGE inverters wired in parallel to supply that much power. Two XW-Pro 6448, or two Outback Radian 8048s are likely to be able to power this.
I'd guestimate that to reliably generate 5000W to run the unit, you'd need about 7500W of panels, on rotating mounts that can track the sun. Here's a mount I designed and built that can hold six large 250W residential panels. You'd need five of them, with a total of 30 250W panels to make the required electricity from 8am till about 4pm, assuming they are in a East-West line. If you want to generate 5000W after 4pm, you can orient the line of your arrays more North-South. It really depends a lot on your array spacing and how far apart they need to be to keep from shading each other. I'd say 20' spacing pole to pole, so a linear line of arrays would take up at least 100' of space.
If you went with roof installation instead of ground mounts, the panel count would go up. Let's say you have open roof space to accomidate panels facing due West. Before noon, the angle of the panels is such that you can't expect more then 25% output. You'd need ~20,000W of panels on a West-facing roof to turn on the air-con at noon. After about 3pm, you are likely to reach at least 50% output, and would only need about 10,000W of panels to start the air-con.
Is this starting to sound very daunting to you? It should be. It might be far more realistic to design a system around keep one or two room cool, rather than the whole house.
