1 Skein of yarn (any color)
Thread to match yarn
Make a chain of slip knots. Cross the end of the yarn over itself forming a circle. Pull your finger thought the circle and take a hold of the the long end of the yarn.
Pull the yarn through the circle until it is tight. Continue making slip knots until the chain is long enough to coil around the whole Kippah.
Start coiling it around the Kippah starting in the center. Sew the coil in place as you go along.
The original Kippah becomes your lining.