Heard about a mod involving a CNC vinyl cutter: the free-rotating blade was swapped out for a wire guide and bearing. The bed, covered with double-stick tape. So, wire sticks to bed, CNC path traces the coil, and winding proceeds. Cover the top with tape, peel it up, and there's your coil. (Think it was on Hackaday?)
You can do this by hand as well, but it may be too tedious to bother with. In that case, the other method mentioned (a conventional bobbin windup, but with the "cheeks" only one wire-width apart, thus giving a single layer pancake winding) will be best. Build the fixture in such a way that you can remove the sides progressively, so you can tape down the winding as you go, without it unraveling.
Tim