As many others have posted, trying to power air conditioning for an extended period of time from a battery bank that one could fit in a typical van is unrealistic. One thing that hasn't been pointed out is that you can't rely on the standard Amp-hour rating of a lead-acid battery when your load is more than its rating, in terms of C/[hours]. For most batteries that are suitable for house use, that's C/20 (i.e., a 100Ah battery can actually support a load of 5 Amps for 20 hours before going dead). If you try to use the same battery to support a 50-Amp load, it will do so for a much shorter time than 2 hours. As an example,
this 100Ah AGM battery has a C/20 Amp-hour rating of 100 Ah. Use it to power a 60-Amp load, and the rating drops to 60Ah. For flooded lead-acid batteries, expect the drop in rating to be even worse, due to higher internal current resistance.
That being said, an evaporative cooler such as the
TurboKool might work, depending on three conditions:
* The humidity in your area is low enough that such a cooler can effectively function
* Your need for stealth doesn't preclude having what looks like an RV roof-mounted air conditioner mounted on your van's roof
* You have enough clean water available for the TurboKool to function properly
Given its rated Amp draw of 4.6 Amps on High, 3.2 Amps on Medium, and 2.2 Amps on Low, you could reasonably expect a 100W PV panel and a 100Ah battery to power a TurboKool on Low throughout the night. Once your battery is fully recharged, you could take advantage of the power still being generated by your PV system to switch a TurboKool to Medium, until the "excess" power generated by your PV system drops back to a level needed to maintain the charge level of your battery bank.
