Got someone who is just a little but handy? We bought (from Wally-Mart) a set of 4 cup holders for auto windows. Screwed a small block of wood to the bottom side, so that the wood would hit the side of the chair, and keep it in the correct position. They come off easily, which is a good thing, as they will usually crash into one side of all the "gates", just makes the chair a tad too wide.
We hang one on each side, one for me, and one for my partner (in the chair).
Total cost? $1.99 for set of two (tossed the other two out) and about 15 minutes time.