My grandmother, most awesome woman ever, if she was alive would be 102 now, used to sing this to me. Now I sent it to my boys at least every week.

Her version went:

Little birdie in the tree, in the tree, in the tree,
Little birdie in the tree Sing a Song for [ child's name ]
Sing about the treetops, over the garden wall
Sing about the sea-ships with there masts so tall, yip,
Little birdie in the tree, in the tree, in the tree,
Little birdie in the tree Sing a Song for [ child's name ]