The melody of "Home on the Range" that we know today dates from 1930. In the 1920's, it was usually sung to a different melody, but the only example I can find on Youtube is this one by
Jules Allen, which is incomplete. I have another recording, from 1928, that uses this melody, but it's on a 78 rpm disc.
Yet another melody, which may be even older, is available on Youtube. Perhaps it's the original.