Lester McFarland and Bob Gardner, known professionally as Mac and Bob recorded "That Little Girl of Mine" which has lyrics similar to if not identical to those requested. The recording was reissued by Old Homestead on LP and was eventually issued on CD. The song was written in 1873 by William S. (Shakespeare) Hays, a prolific and popular song writer in the 19th century who also wrote "Molly Darling". Mac and Bob and Gene Autry, as well, were on the WLS National Barndance so their music was widely distributed over the airways and both sold a lot of recordings although Gene outsold Mac and Bob by far.

Here is a link to Mac and Bob singing Faded Rose and a Broken Heart.

Mac and Bob