Here's one of my favorite versions from American Memory colection from the 1840's to 1860's, no date given. Published Boston, Massachusetts by L. Deming.

BARNEY, LEAVE THE GIRLS ALONE,

JUDY leads me such a life, (repeat)
The devil ne'er had such a wife,
What can the matter be?
For if I sing the funny song
Of Dolly put the kettle on,
She's mocking at me all day long;
What can the matter be?

SPOKEN.--Yes, she does lead me a devil of a life, that's certain, for we never walk out on Sunday, but what she makes me walk behind, and carry her parasol and reticule, which makes me look quite ridiculous; and if I happens to cast a sheep's eye at any of the girls as they pass along, my wife is sure to bawl out,

Mr. Barney, leave the girls alone! (repeat)
Why don't you leave the girls alone,
And let them quiet be?
Put the muffins down to roast, (repeat)
Blow the fire and make the toast;
We'll all take tea.
O, Barney you're a wicked boy, (repeat)
And you do always play and toy
With all gals you see.

SPOKEN.--When Mr. Barney was a young man, he was the handsomest, most modest, most refined and delicate person I ever met with; but now he's every thing that he ought not to be. My wife is the very devil, especially when she's in bad humor. You must know the other afternoon I was ax'd out to take a comfortable dish of four shilling souchong tea, none but the best. As bad luck will have it, my wife Judy, was along; but notwithstanding, I got seated along side of a pretty girl. I saw she got smitten with my countenance. Said she, Mr. Barney, will you have a game of hunt the slipper? With all my heart, says I. So as I was just a making a preparation to do the thing in a genteel way, Mistress Judy, who had seen the operation from the other end of the parlor, was so ungenteel as to bawl out,

Mr. Barney, leave the girls alone, (repeat)
Why don't you leave the girls alone,
And let them quiet be?
O, Judy, you're a pretty child, (repeat)
I have my fears that you'll get spoil'd,
If you should have your way.
Barney, rock the cradle, O, (repeat)
Or else you'll get the ladle, O,
When Judy harps to-day.

SPOKEN.--Barney, if you don't rock the cradle, I'll break your pate with a ladle; I'll comb your head with a three legged stool, I will, so I will. Now that's the way we go, to be sure, and to say the truth, its none of the pleasantest. You see I loves a good dinner, but some how or other, we don't get much in the week days, a pig's foot, and a carrot, no great choice; but on Sundays, we generally have a shoulder of mutton, stuck round with turnips. I like a piece of the brown, but my wife always carves from choice. So says I, my dear, I always call her my dear, at dinner time, I should like a piece of that. I'll give you a piece of that, said she, and up with a dumpling plate, and let it fly at my head, while she kept time with her old tune of

Mr. Barney, leave the girls alone, (repeat)
Why don't you leave the girls alone,
And let them quiet be?
Judy she loves whiskey, O, (repeat)
She goes to uncles shop at night,
And spends an hour or two.
Then Barney, what must Barney do,
But take a drop of whiskey too,
And toast the girl that's kind and true,
For that's the way with me.

SPOKEN.--Yes, the other night I was ax'd out with a few of my old acquaintances; there was Jo Snap, the chimney sweeper, and a few others, particular friends of mine. As soon as I got into the room, one of the girls says, there's Barney, that handsome, delicate, discreet young man. There was among the rest, Miss Polly Smallfry; now the last time that I had seen Polly, she was leaning her beautiful black arm over a keg of pickled oysters. Says she to me, Barney, she alwas called me Barney, there's no fear but what you'll get along in this world, as long as you're so polite. Polly said so. Says I, Polly, we are neither of us rich, but if you have no objection we will trust to providence, and I will make you my spouse; but just at that instant, who should pop into the room, but her mother, and with a very gentle, delicate voice, says, Polly, don't you go for to make another d--d Judy of yourself, there is time enough for you to get married, when you find one who has something that will make the pot boil. That was a damper. Her mother soon retired, and says I Polly, I think I can express myself better to your satisfaction than that, and was just going to give her one of my mortal hugs, when, who but my wife, should stick her long snout through a pane of broken glass, with that infernal old tune of,

Mr. Barney leave the girls alone, (repeat)
Why don't you leave the girls alone,
And let them quiet be.

-Richie