Yankie, I think "Little Potato" was written by Pete Sutherland, and is on one of his recordings with Malcolm Dalgleish and Grey Larson (the trio sometimes went by the name Metamora, but I have a vague memory the song is on an album by just Dalgleish and Larson). I'll see if I have it at home, and post the lyrics if I do.
Another fun song to sing is "The Baby Tree"; it's a traditional song, but my only recording of it is on Paul Kantner's (of Jefferson Airplane fame) "Blows Against the Empire". I'm surprised it's not in the DT; I'll try to add it, too.
Finally, you'll be needing a supply of what Raosalie Sorrels calls "hostile Baby-rocking songs"; the songs you sing when you're aching with lack of sleep and frustration describing all the horrible things you'd LIKE to do to the kid (but won't, 'cause you're taking out your hostility by singing the song). For example,
This is the day we give babies away
With a half a pound of tea
If you know any ladies who want any babies
Just send them all to me.
Good luck and much joy to all three of you!