Try a traditional version from Traveller Mary Delaney.

Jim Carroll
In Charlestown there dwelled a lass,
She was as constant as she was true,
When the young man fell in courting her
And drew her in despair.
               
He courted her oh, for six long months
And to him she proved unkind,
He courted her for six long months
And by him she proved a child.

Go home; go home to your dwelling place
And don't bring your parients in disgrace.
Oh go home to your dwelling place
And you proved with a false young man.   
                  
Now I will not go home to my dwelling place
For to bring my parients in disgrace,
I'd sooner go and drown myself
In a dark and a lonely place.

Now he catch her by the yellow locks
And he drew her along the ground,
Till he brung her to the river
Where her body cannot be found.

Oh down she goes on her bended knees,
Oh, for mercy she loudly cried,
Saying, Willie dear, don't murder me,
And I am not fit to die.

Now as Willie went out walking,
He went out to take fresh air
And he seen his own love Mary
In the waves of the silvery tide.
                  
Oh, he strips off his fine clothing,
To the river brim he swum
And he brung his own love Mary
From the waves of the silvery tide.

Mary, darling Mary,
Is this what you have done
And the last words I have said to you
I just said it for fun

The usual story to this song is that Mary is courted by Willie, but is seduced and made pregnant by a rich nobleman who then murders her and throws her into the river.
The body is found by Willie, the murderer is discovered and hanged.
Somewhere in its development, Mary Delaney's version has lost the third character, the seducer, and Willie is given as the murderer.
The song has not turned up very often in published collections in Britain or Ireland and it has been said to be fairly rare in the U.S. having been included in only a few works there.   It seems to have been known by seamen including those working in the whaling trade as it appears in two collections of sailors' songs.
Reference.
Shanty Men And Shanty Boys    William Main Doerflinger
Songs The Whalemen Sang            Gale Huntington