Find something round to use as a template . Trace and cut out so that the hole remains intact.
Use the pattern with the hole as a viewfinder.
Now place the button into the hole, remove the pattern and draw a circle about 1 cms away from the circumference. Use the button to make exact size patterns on a piece of thick cardboard and polyester batting.
Sew around the fabric scrap, about 1/2 cms away from the edges. Do not secure the last stitch and leave the needle threaded.
Put the batting inside the back side of the fabric scrap, top it with the cardboard piece, and pull . It should look like a bottle cap.
Secure by sewing zigzag all around. ( This is the tricky part as to whether the button will turn out round or not. )
Now place the newly sewn button on top of some felt. Trace and cut out. Fold the felt in half, and make 2 snips vertically. This will become a slot to put the hair clip in.
Glue the button onto the clip.