The readings for this one are the kun'yomi readings of each kanji. 子 is just こ, like the individual vocab word. 供 is ども, however. Remember this by thinking how much children love domo-kun.

Also, 子ども is kind of more "politically correct" with the kana hanging off there. 子供 is still used in a lot of situations, usually stiff ones. The second kanji means servant, and some people don't like that. The second version pops up a decent amount, so it's good to be familiar with that as well.