If you really want to do it, though, you'd probably have to knit to the size of the seat.
Measure the seat front, check your guage, then cast on X stitches and knit to the height of the seat adding in any shaping needed, probably just needed near the top.
You could pick up stitches around 3 edges for the side pieces. and make a duplicate of the front piece for the back and sew it on. Ditto with the seat, though of course you'd only need the top and 3 sides. Make some I-cord ties to tighten everything together.