I have the same need. Problem is that the flip-down couch is upholstered on that side of the stairwell, and I don't like messing with the upholstery. I am thinking of fabricating a metal hook (that sort of thing I *DO*), for the top end, to slide over the upholstery.
For the bottom end, either a swiveling mount, or a sliding tab. (tab A inserted into slot B). The top mount will support weight. Think 3-4 inch flat stock, bent to fit over the couch side at the top and attached to the top rail mount. with the bottom rail-mount solidly fixed---- should be strong, removable, unobtrusive, cheap, and a great show- and -tell around the campfire.
the hook to slide over the upholstery can be padded, or peel-and-stick protection applied to the upholstered edge of the couch, for protection. (Or both)