I did a google and found the following site, that has quite a few listings for children's sock/stockings;
http://www.knittingpatterncentral.com/directory/socks.php

Sylvia, try making them with two strands of fingering held together. Usually, two strands of fingering is about the same as DK weight. I know it's a lot of work for an experiment, but it's worth a try. I had a pattern for a baby sock made out of DK, but have no idea where it is.

Tami

Tami, good suggestion of doubling up with the fingering yarn. Actually I have a few balls of wool that would look nice combined for a tweedy effect. Probably a good way to use up some of "all that darn yarn" as my better half says.
Sandra, I did check out your suggested website and found the children sock patterns. I printed off a few for further reference.
Thanks ladies for taking the time for me.