Here's an easy sock pattern using two needles. I think this might be for an adult. You could probably get the yarn type, needle size, and number of cast on stitches from any child's sock pattern. Adapt it for this method. Looks pretty straight forward.
http://www.bevscountrycottage.com/kp2.html
http://www.copdandsomuchmore.com/pat...kchildtwo.html