Eddie, is there any where around you that sells furniture in flatpack boxes (e.g. Ikea?). If you could get one of the boxes that pre-assembled bookcases or something come in, you could make that light tight and string some wire/string/fishing line inside to hang paper. Standing up vertically, the narrowness of the box would allow it to be put behind a bench or whatever to keep it upright and out of the way while still leaving just enough room inside to keep the paper from sticking to anything while it dries.
Just a thought, no personal experience of my own in this area. Of course, an empty, unused cupboard would probably be a lot easier and leave you with a less DIY look to the end result