I just bought the rare "The Berry Tree" 45 rpm for $3.00 from an Internet site:

Cadence-1261 Bill Hayes Blue black hair/The berry tree DJ VG++ $3

It was written by Saul Chaplin (Saul Kaplin)

From Sonwriters Hall of Fame:

{Quote}

Saul Chaplin was born Saul Kaplin in Brooklyn, New York on February 19, 1912, and attended New York University's School of Commerce with the intention of becoming an accountant. A self-taught pianist, he earned money while in school by playing with local bands. One night in 1933 he was approached by another band member, Sammy Kahn, who suggested they try writing songs together.

They quickly discovered that they enjoyed working together, and soon they were writing as many as ten songs a day. The twosome made money for a time as writers of special material for entertainers at resorts in the Catskills and in 1934 they had their first published song, "Rhythm Is Our Business", which became a Number I hit for bandleader Jimmy Lunceford. In the process, they ceased to be Kahn and Kaplin, changing their names to Sammy Cahn and Saul Chaplin.

{End Quote}

The Berry Tree charted at #43 in 1955 and it was sung by Bill Hayes who had a #1 hit in '55 with THE BALLAD OF DAVY CROCKETT.

My long search is finally complete: I taped the movie the song was the theme of "Many Rivers To Cross" and I bought the song a few days later. This search would have been impossible without the Internet, what a great tool.