These cots are pretty nice, comfy, and about the size you're looking for:
http://www.walmart.com/ip/Coleman-Comfortsmart-Folding-Camping-Cot/20594108
If I'm building a bed from scratch, my preferred method is to build the frame out of metal conduit, and then string it with rope to support whatever mattress you decide to use. This method should make you an extremely durable, yet lightweight bed that should last a lifetime. Using this method, it is pretty simple and easy to construct a lightweight bed of any length, width, and height to fit your space.
Any hardware type store, or Home Depot type store should have everything you need to make thee frame, then I use dollar store rope to string them.
With only slightly more difficulty, you could make it foldable as well.
Another option is to pick up a used Hollywood style bed frame such as this one:
https://seattle.craigslist.org/kit/fuo/5462808169.html
Totally adjustable for width, and then you can string it with rope to support a foam mattress. You can add conduit or pipe to the legs, to make it higher for added storage underneath.