It's called "The Jolly Boatswain" in Cazden/Haufrecht/Studer Folk Songs of the Catskills, which also has a related song, The Trooper and the Tailor, which is in the Digital Tradition.
^^
The Jolly Boatswain
(as sung by George Edwards)

1. There was a jolly boatswain in our town did dwell,
He had a loving wife, and the boatswain loved her well.

Refrain:
Fal di roddy, too-la roddy,
Fal di roddy, too-la ray.

2. As she went a-walking up and down the street,
The handsome little tailor she chanced for to meet.
She says, "My dearest husband has gone off to sea,
If you've no other place, you can lodge along with me!"
(Refrain)

3. He went home with her to lie that night,
When the husband put the couple in a devil of a fright;
About ten o'clock at night they heard a rap at the door,
This little tailor boy couldn't sleep no more.
(Refrain)

4. So they got right up, being half asleep;
Says he to her, "Where the devil will I creep?"
They got right up, being half undressed,
Saying, "I know of no place, only over in the chest."
(Refrain)

5. She put him in the chest amongst a lot of things,
And she ran downstairs for to let her husband in;
She ran downstairs, she unbolted the door,
And there stood her husband and seven sailors more.
(Refrain)

6. She hugged him, she kissed him, she gave him a caress,
Says she, "My dearest husband, what's the meaning of all this?"
"I haven't come to rob you, nor 'sturb you from your rest,
But I'm bound for the sea, and I've come for my chest."
(Refrain)

7. He goes upstairs with his seven sailors strong,
[They] grabbed right aholt and they yanked it right along.
(Refrain)

8. They hadn't gotten more than halfway to town
Fore the heft of the chest caused the sweat to run down;
They went a little further and they sat them down to rest,
Says one to the other, "What the devil's in the chest?"
(Refrain)

9. They sot down the chest and they lifted the lid:
There sat the tailor lad a-scratching on his head.
(Refrain)

10. Says, "I'll take you down to Chiny, I'll trade you for tea,
If I don't punish you, might the Devil punish me!"
(Refrain)

11. So he took him down to Chiny and traded him for tea,
And they had enough tea for to hold your company!
(Refrain)

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Note that the tune is for the second verse. You have to make your own adapatation for the two-line verses.

Click to play