When my children were young enough to be sung to sleep, I did not limit myself to lullabies. Any quiet song with a repetitive melody seemed fine. I found spirituals to be wonderful resources. My favorite to sing to my two boys was "Oh, Freedom". It is in the DT. I could not follow the tune in the midi that is offered there, but it would be a start. I remember it best from the singing of Odetta.
Roger in Baltimore