There are 1001 songs of separation and sadness. They all begin to sound alike if you look at enough of them.
One that is found from the Appalachians to the Ozarks is "Little Darling," or "Don't Forget Me, Little Darling." A version with audio is in Max Hunter. First verse:

Don't forget me, little darling
When from you I'm far away
Just remember little darling
We will meet again someday.
Also:
Who will teach you little darling
Who will hold you to their breast
Who will talk the future over
While I roam the desert west.

At my window proud and lonely,
Ofen do I think of thee
E'r I wondered little darling
If you ever think of me.

Several ballads have "night birds singing," including "Love Me at Twilight." It is easy to mix and match these songs.

The main difference in "Rough and Rocky Road" is the reference to "Don't my baby look the sweetest when she's in my arms asleep." This refers to the lover, but has a reference to a child been lost?