I am in mostly the same boat as you. My house doesn't have central air - well, it has a hookup for it, but it's a long story as to why we don't have it hooked up, and the end result is because I am cheap.
I don't know where you're at, but I'm in southwestern PA, and it's really only about three to four months of the year when it's too darn hot for sleeping without AC. At least, it is for me, after growing up in Colorado where it's hot but dry. The humidity is really what kills me out here.
I have window units in each of the three bedrooms in the upstairs of my house. Before I get taken to task, though, I got one for free from a co-worker and paid $60 apiece for the other two. I haven't had a single problem with any of the units, even though one of them is super, super old. Plus our power bill in the summer is always less, even though I usually run the AC unit all night.
I'm sure that I could optimize these options, but they are what works for me right now.
I would advise you to pick up a used window unit on Craigslist.