You might already own a punch and want to start making buttons made with fabric. If this is the case, you can try to slide the material through the punch to cut it into circles. Like I mentioned before, you can place tape on both ends to pull the fabric through.
Again this may or may not work depending on the thickness of your fabric and if you have embroidery work on the fabric.
Coming Soon ….
Using Fabric on Mirror Back buttons
Make Pacifier Holders with Clip On Buttons