Pool Noodle Seat
Grab a pool noodle and bend it into the shape of a horseshoe around the seat of the chair. (It should sit on the seat like a cushion.) Cut off the ends of the noodle where they meet the edge of the seat. You can use duct tape to secure the noodle to the sides and back of the chair.
You could also loop the noodle into a circle, tape the ends together and then tape it to the seat of the chair. Experiment to see what works with the chair.