My youngest child always liked a song or story at bedtime and the range he liked was huge!
He liked his dad to sing him 'Ride On' or some fairly rousing songs (at bedtime? - I know!); his older sister used to sing 'The Spinning Wheel', or 'Sonny' or something by Fairground Attraction.
His favourites from me were 'The King of Rome' or a song which actually was a lullaby, or at least like a lullaby: 'Waiting for the Lark'.
The only recording I have of this is by June Tabor and I think it might be on 'Against the Stream'. I can provide lyrics if you'd like them.
I have words for other lullabies, including the Miner's Lullaby and some in Gaelic. I could maybe scan in the tunes. I don't know of recordings, though.
PM your email address if you want any of these.
Enjoy your grandchild and sing anything you like to him.