this happened to me a few months back. an early 70s schwinn super sport with hookless rims. I tried a couple of different tires but that didnt change things. after blowing 4 or 5 tubes I decided to buy a new wheel figuring my tube expense would soon exceed the price of the wheel. niagara has a decent rear wheel (alloy rim, 36h, ss spokes) for just under 40 bucks shipped when ordered through amazon. once i put the tires on the new wheel I had no more blow outs.

http://www.amazon.com/gp/product/B00...00_i00_details

be sure to destress the spokes if you go this route