Here's a great haunting variant:

I heard it it on the radio, later Ned Oldham sang me the Child #20 version which I think I prefer.

as performed by Tim Eriksen on A Prairie Home Companion, October 29, 2005 -
http://prairiehome.publicradio.org/programs/2005/10/29/

Two Babes

In New York there was a lady fair
All alone and a loney,
Was then she had two pretty little babes
All down by the greenwood sidey.

She had an apron old and worn
To wrap these two pretty babies in

She had her knife both long and sharp
She pierced them to their tender hearts

She dug a grave both wide and deep
She laid them down and she bade them sleep

As she was turning home one night
Was there she saw these two pretty babes

Oh babes, oh babes, if you were mine
I'd dress you in all silk so fine

Oh, Mother dear, we once were thine
And neither dressed us course nor fine

You dug our grave both wide and deep
You laid us down and you bade us sleep