The Leo Maguire version in the DT is brief, so not quite sure what you are looking for. Are they songs with the verse about never having loved the baby, etc.? Or whether the father or the lord is searching? Saddling a steed? Gloves?

Most of these songs in America were collected in the 20th century. Although the singer may refer to 19th C. origins one can never be certain, nor can they be placed in chronological order.
The Max Hunter Collection has six versions: Gypsy etc

Vance Randolph has seven in his Ozark Folksongs. They all seem singable to the tune used by most singers.
The Frank C. Brown Collection of North Carolina Folklore gives music for 13 versions (vol. 4). On page 84 is the comment that the melodies have much in common with "Der mey hat menig Herze hoch ersteiget, which was composed by Neithart von Reuenthal (1180-1240)." Differences seem to be based on the singers abilities or search for emphasis rather than on inherent differences in the melody or meter.
Give me more details of what you are looking for and I will try to find it in these references.