You can hear a recording of THEY CUT DOWN THE OLD PINE TREE sung by the Carson Robison Trio on April 30, 1930 at The Internet Archive. It reveals an important error in the lyrics in the DT. It should be

There'll be no cabin [not "coffin"] of pine
For that sweetheart of mine.

THEY CUT DOWN THE OLD PINE TREE was also recorded by Gene Autry, Black & White, Buck Wilson & His Rangers, Dan Parker w/Orch, Dick Robertson w/Orch, Frank Luther, Frankie Marvin, Gene Carroll - Glen Rowell, Hart & Ogle, Joe Rines & His Orch, Louisiana Rounders, Paul Mason, Redd Evans & His Billy Boys, Rice Brothers Gang, Tennessee Moonbeams, Tommy & Willie, Tune Wranglers. This information is from the Online 78-rpm Discographical Project.