Greetings:

Here is how I worked it out in D. Each chord change is indicated to the immediate left of the syllable where it occurs.

[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 [C]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 [C]Tennessee [D]Stud.

Chorus:
Tennessee Stud was [F]long and lean,
The [C]color of the Sun and his [B-flat]eyes were [A]green.
[run down as chord changes from A to D: a - g - f - e - d]
[D]He had the nerve and he had the blood,
And there never was a horse like the [C]Tennessee [D]Stud.
No, there never was a horse like the [C]Tennessee [D]Stud.

You can play an F chord in place of the B-flat in the chorus. Whatever you decide, just make sure that d note at the end of the descending run coincides with the chord change from A to D. Begin the run on the 3rd string stopped at the 2nd fret. You will be singing a d note on the word "He" in "He had the nerve..." and it will be in unison with the d note which ends the run, i.e. the 4th string played open.

That last line in the chorus is an optional repeat. You can use it or not as you choose.

--- Steve