I had a problem with some stains on my stools, so I decided that I should make a removable cover... Mushroom-like cover seemed like the best option. I did this project long time ago, so I don't have any pictures of making it, but it is really easy and I don't think that you will have the problem making it.
Measure the size of the top pillow on your stool. Mine are in form of cube, so i measured it diagonally and added about 10 inches.
Cut the red material for the stools. I cut mine in form of the circle with the diameter long as the diagonal of the top of the stool.
Stitch the string or some long elastic band around the edge of the material for cover, leaving the ends of the strings out, so that you could tighten it later when you put it on the stool.
Add some white circles made from your old white T shirt, or some other old material.
Put it on the top of your stool and tighten it up, pulling the ends of the string that you left before. I added an extra pillow before putting the cover on because the stool was too flat, and I wanted to make it to look more like mushrooms.