@freemo From the Christian things I've been to, my impression is that prayers addressed to baby Jesus relate to things like innocence, purity, and so forth - that is, concepts associated with childhood. Prayers for strength and the like would tend to be addressed to Jesus from the Last Supper to the Crucifixion, and prayers for the departed to Jesus in Heaven.

However, a friend of mine started seminary this month, who will probably know more. I'll pass along any additional info she gives me.