Malvina wrote it. It was one of the first songs she wrote (it was about her daughter) and when she went to get it published people told her she had to have other names on the copyright as well. (Because.) Currently she and a man named Alan Green share the copyright. He "arranged" it, and made out like a bandit from the money it made when Harry Belafonte recorded it.
Malvina had an interesting singing voice, but not a particularly good one.
I just went and looked it up in her songbook, and Harry is NOT included on the copyright, but he may have been on earlier versions. If so, they may have renegotiated the deal, but Mal and Mal alone wrote it. Some of her other early songs also have/had joint copyrights -- Little Boxes is also in Pete Seeger's name.
Blessings,
Barbara