"Mary's Little Boy Child" is the legal title of the Jester Hairston song. ASCAP # 430205084. The variation "Mary's Boy Child" and a couple of other variants are listed for the same number.

There are eight BMI listed songs with the legal title "Mary's Boy Child," by various composers. No relation to the Hairston song.

"Oh My Lord" was *composed by Frank Farian and F. Jay, but the tune used may be trad. Composers from CBC track listing (and another site listing only Farian):
http://www.cbc/radioshows/SHIFT_NB/20091222.shtml

*More information needed. There are several songs with that or similar title, including a spiritual.