I have only seen snippets of this movie. And, I do not know the history of Wyat Erp and the OK Corral. But, how/why can a Miner 49 (of the San Francisco gold rush) be in Tombstone AZ? Maybe some pilgrim can set me straight (he turns, spits on the ground).
Well? You boys gonna pull them pistols, or whistle “Dixie”? 
Yeah, that’s the ticket, doc! They were excavating in a cavern, in a canyon, excavating by a crater; lived a miner 69er and his daughter roboto, Clementine
(Roberto Clemente, you say?) Oh my darlin’, …
Now, if anyone else has a reply that isn’t too spaced out…
I can share with you the movie cast Henry Fonda.
Simplest answer: the title is a conceit of John Ford’s.
If you go to IMDb, you’ll see that, ta da! Cathy Downs played the part of “Clementine Carter.”
There’s a girl named Clementine so they can play the song and give the movie the title. If you want to go farther than that, there’s this from Roger Ebert’s Great Movies page:
Ebert is dead wrong. The movie is NOT about Clementine – she’s actually a fairly minor character, other than having her name as the title. She’s there primarily so that there can be an entirely unrealized romance between her and Wyatt (Henry Fonda.)
Incidentally, the film has a truly evil and wonderfully wicked villain, played by Walter Brennan – an astounding performance.
BTW, a miner (a '49er) could certainly have a daughter alive in 1881. The song doesn’t say that she was born in '49, only that the father emigrated to California in '49.
I always thought of the concept of Clementine (the song) as a metaphor for for Earp’s moral code as conceptualized by Ford and manifested by Fonda. It was simplistic but very widespread. It dealt with death and acceptance of it.
I always thought that Ford put the character name in to reinforce the the metaphor created with the song and title.
Just a thought.
TV
Ford liked the use of “old West songs” as symbols in his films. The title “She Wore a Yellow Ribbon” came from a song popular on the plains. In another film he had John Wayne constantly humming “Pretty Redwing” throughout the film, another song that was popular in dance halls and the like. In yet another the song was “Buffalo Gals.” As I remember Wayne was the one who sang it there also, but I could be wrong.
Perhaps it was a throw back to the singing cowboy, but I feel the songs meant more than that. They were key symbols in Ford’s films. They set the pace and gave clues to the feeling that under lay the film.
TV
“Hmmm,” [the Vogon] said, “counterpoint the surrealism of the underlying metaphor…” He considered this for a moment, and then closed the book with a grim smile.
“Death’s too good for them,” he said.