Looking through my notebooks of trivia garnered from the net, I found that someone on a newsgroup had suggested the following for the last two lines of the Carters vocalising towards the end:

Riding of the goat, leading of the sheep
Won't be back 'fore the middle of the week

Listening again, 'sheep' seems right and certainly is more appropriate in this rural context, but I hear it the other way round: 'Leading of the goat and riding of the sheep'. And I reckon it is: 'Ain't gonna be back ['fore] the middle of the week'. Anyone else willing to lend their ears to this? It doesn't really matter - you can sing any nonsense - but it is a challenge.

--Stewie.