The DT has it as Red Apple Juice. Lyrics are similar to a version of "Red Rockin Chair," attributed to Lily Mae Ledford of the Coon Creek Girls, but neither mentions Jericho, so I 'spect you're looking for another variant:

RED ROCKING CHAIR

1. I ain't got no use for the little red rockin' chair
Got no sugar honey baby here
Who'll rock the cradle, who'll sing that song?
Who'll rock that cradle when you're gone?

2. I ain't got no use for the little red rockin' chair
Got no sugar honey baby here
I'll rock the cradle; I'll sing that song.
I'll rock that cradle when you're gone.

3. I've done all I can do, said all I can say
Take you to your mammy next payday.
I'll rock the cradle; I'll sing that song.
I'll rock that cradle when you're gone.