I normally play this song in the Key of B, here are the chords I use:
(The F# can be played as an F#7)

[B]Along about eighteen twenty-five,
I [A]left Tennessee very much alive.
I [B]never would have made it through the Arkansas mud,
If I hadn't been riding on the [F#]Tennessee [B]Stud.
I had some trouble with my sweetheart's pa,
[A]One of her brothers was a bad outlaw,
So I [B]sent her a letter by my Uncle Fudd,
And I rode away on the [F#]Tennessee [B]Stud.

Chorus:
Tennessee Stud was [A]long and [B]lean,
The [E]color of the Sun and his [D]eyes were [F#]green.
[B]He had the nerve and [A]he had the [B]blood,
And there never was a horse like the [F#]Tennessee [B]Stud.

The chord progression is a little different, so here is how it would
look like in D, as you have it in D above.

[D]Along about eighteen twenty-five,
I [C]left Tennessee very much alive.
I [D]never would have made it through the Arkansas mud,
If I hadn't been riding on the [A]Tennessee [D]Stud.
I had some trouble with my sweetheart's pa,
[C]One of her brothers was a bad outlaw,
So I [D]sent her a letter by my Uncle Fudd,
And I rode away on the [A]Tennessee [B]Stud.

Chorus:
Tennessee Stud was [C]long and [D]lean,
The [G]color of the Sun and his [F]eyes were [A]green.
[D]He had the nerve and [C]he had the [D]blood,
And there never was a horse like the [A]Tennessee [D]Stud.

These chord changes may sound better in the Key of B, either using
those chords, or capoing to the second fret and playing A.