I came across the idea of making leather mushrooms here. I have a box of leather scraps (remnants from a furniture factory) that yielded perfect materials, but vinyl would work just as well. These were very easy to make and quick (except for the time needed to allow the glue to dry). I used Gorilla Glue, but I've read that rubber cement also works well for gluing leather as long as little strain is put on the bond. If you've tried using rubber cement on leather, please let us know how well it worked for you in the comment section.
Once the glue on the mushroom cap is completely dry, stuff it. I used diy recycled stuffing made from thinly cut strips of plastic grocery bag, but poly fill or wool would work equally well. Stuffing is inserted into the cap through the X-shaped slits you made before gluing the top and bottom of the cap together.