Here is another version I heard in Belfast, it's titled " All Round The Loney O" I would imagine there are hundreds of versions, in Ireland, England, Scotland, Canada and the U.S.A.

ALL ROUND THE LONEY O

There were two sisters going to school
All round the Loney O
They spied a woman at a pool
Down by the greenwood sidey O

She held a baby on her knee
All round the Loney O
A cruel penknife they could see
Down by the greenwood sidey O

She held the baby to her heart
All round the Loney O
She cried "My Dear, we both must part"
Down by the greenwood sidey O

She held the baby to her breast
All round the loney O
She said "my dear we'll both find rest"
Down by the greenwood sidey O

There is a river running deep
All round the Loney O
It's there both baby and mother sleep
Down by the greenwood sidey O