Here's the rhythm as it is in my piano book (I had to squeeze the top line a bit to accommodate the up-beat). It's in G major in my book, but I transposed it to F major because that's the key the Byrds' version is in:
The Byrds' version alternates between instrumental sections (where the melody is played on twelve-string guitar) and sections that are sung. There are three of these instrumental sections, and the first and third are the same (the guitar part is, at least), but the second is slightly different. Here's the notation for the first and third iterations:
Compared to Foster's rhythms, the Byrds' version is more syncopated. In the third measure in each line, two of Foster's quarter notes are turned into a dotted quarter note followed by an eighth note, and there's a similar shift in rhythm in the second measure of the third line.
That second measure of the third line is the only difference in the second iteration of the instrumental section. In the first and third iterations, there's a half note tied to an eighth note followed by a second eighth note, but in the second, it's a dotted half note:
In my piano book, the song is played with only three chords (I, IV, and V7), ostensibly because it's a book for beginners. The Byrds' version of "Oh, Susannah," however, involves six chords (played only during the sections that are sung):
F major | A minor | D minor | G major
F major | A minor | D minor | G major | F major
Bb major | F major | C major
F major | A minor | D minor | G major | F major
The coda is Bb major to F major.
