Tell Me That You Loved Me is a song by Will S. Hayes written in 1866 that's titled "We Parted By The Riverside." The sheet music is at the Levy Collection which can't be linked.

The Carters title was probably to prevent copyright/royalty problems as the song had already been recorded by Stoneman and then Kincaid as "We Parted By The Riverside."

TELL ME THAT YOU LOVE ME- Carter Family 1932

               We parted by the riverside
               The moon looked down on you and me
               The stars put on a look of pride
               The river murmured to the sea

               The dew drops kissed the blushing rose
               The mournful winds did sigh
               One word broke nature's sweet repose
               That sad word was goodbye

                   Oh, tell me that you love me yet
                   For, oh, this parting gives me pain
                   Please tell me that you'll not forget
                   For we may never meet again

[INSTRUMENTAL BREAK]

               We parted by the riverside
               Though I have roamed in distant climes
               My heart has not forgot its pride
               For I have loved you all the time

               And I am faithful to you still
               As long as you are true
               Let fate bring to me what it will
               For I love you, only you

                   Oh, tell me that you love me yet
                   For, oh, this parting gives me pain
                   Please tell me that you'll not forget
                   For we may never meet again

                   [INSTRUMENTAL BREAK]

                   Oh, tell me that you love me yet
                   For, oh, this parting gives me pain
                   Please tell me that you'll not forget
                   For we may never meet again