Thanks Georgina, Richard, and Reinhard. Now I can hear that he is singing "Aye, and soon to the church they did go". The pronunciation of the vowel in "soon" threw me.

Comparing my transcription with your @Reinard I noticed other small differences, which may only be on that recording. I have capitalized them.

My sweetheart, come along, can’t you hear the FOND song
The sweet notes of the nightingale flow?
Can’t you hear the fond tale of the sweet nightingale
|: As she sings in the valley below. :|

PREPARE TO IT UNVEIL, for I’ll carry your pail
SAFE home to your cot as we go.
You shall hear the fond tale of the sweet nightingale
|: As she sings in the valley below. :|

Pray, let me alone. I have hands of my own.
And along with you, Sir, I’ll not go.
For to hear the fond tale of the sweet nightingale
|: As she sings in the valley below. :|

Pray, sit yourself down (HERE) with me on the ground
On this bank, where the wild primrose grow.
You shall hear the fond tale of the sweet nightingale
|: As she sings in the valley below. :|

This couple agreed to get married with speed,
Aye, and soon to the [E] church they did go.
No more is she afraid for to walk in the shade
|: Or to sit in the valley below. :|