The best way to stay cool is to use evaporative cooling or a swamp coolers . Yup, you guessed it, ours broke down this past week! Luckily we have two A/C's but unluckily it was our sleeping quarter A/C's that broke down.
Many people told us about "Swamp Coolers" (Evaporative Coolers) in the past. Evaporative coolers are fans that blow out water. They work best in dryer climates with windows and doors open right in front of the unit so they can draw in the hot, dry (not moist or humid air. The best thing to do is run your evaporative cooler during the night, when it is cooler and then trap the moist cool air in the house. You can also add ice to most units to maximize the cooling effect. Evaporative cooling only lowers the temperature by 10-20 degrees depending on the unit, humidity and size of the area you are cooling. So it won't be as cold as A/C but it will make a difference.
You can buy portable units at large hardware stores like Home Depot & Lowes. Unfortunately, their units are not small portable units for the most part. You can buy smaller portable units at online specialty sites such as this. Unfortunately the portable units can only cool areas of only 200-400 square feet. Some of the smaller units are cheaper than ceiling fans so it wouldn't hurt to buy a couple to have them around and use them during the "less hot" summer months.
Evaporative Cooling units are a little less harsh on the environment because they use way less electricity, no freon or refrigerants. They do use a ton of water though. Ours chugs through about 5 gallons of water a day.
All the Best,
I think in the humid south this is not a viable options. It would just be even more sticky. Although we don't seem to have any humdity this year because of the drought.