I think Red Rocking Chair becomes Red Apple Juice because of the rhyme with "I've got no use..."

The Dock Boggs version of this song makes it most clear, this is a song about a prostitute. He is paying for sex. In another version the rounder steals his money and he can't afford to have sex, leading to his further frustration.

"Laid her in the shade, gave her every dime I made"

"And I can't make a living with you"

Red Rocking Chair, Red Apple Juice etc are euphemisms for sex. Rocking in the first half of the 20th century almost always eludes to Moses on the rock where he sees Israel, and simultaneously means the sex act. It is a common double entendre in blues and later became a music genre name (see Sister Rosetta Tharpe "Rock Me"). Not the first American music genre named after something sexual: Jass.

The banjo as we know was originally an instrument invented by african slaves in America, we know that Dock Boggs followed around an African American named "Go Lightning" to learn his picking style, there is no reason the sexual double entendre style didn't make it into bluegrass, country etc.

SUGAR BABY (Dock Boggs, traditional)

Sugar Baby

Oh I've got no sugar baby now
All I can do is to seek peace with you
And I can't get along this a-way
Can't get along this a-way

All I can do, I've said all I can say
I'll send it to your mama next payday
Send you to your mama next payday.

I got no use for the red rockin' chair,
I've got no honey baby now
Got no sugar baby now

Who'll rock the cradle, who'll sing the song
Who'll rock the cradle when I'm gone
Who'll rock the cradle when I'm gone?
I'll rock the cradle, I'll sing the song
I'll rock the cradle when you gone.

It's all I can do
It's all I can say,
I will send you to your mama next payday

Laid her in the shade, give her every dime I made
What more could a poor boy do
What more could a poor boy do?

Oh I've got no honey baby now
Got no sugar baby now

Said all I can say, I've done all I can do
And I can't make a living with you