The first version posted by Dicho is from the Walt Disney film starring Fess Parker and Buddy Epson. I assume the melody was composed for the film.
I'm delighted to learn that Crockett actually wrote the poem. I had always assumed the whole thing was made up by Hollywood so they could throw a song into the middle of an otherwise "cool" western. As a kid, I always hated that. The bad part of Martin & Lewis films (for a kid) was when Martin would sing.
Thanks Guest,BigDaddy for starting the thread.