Malcolm (and Amos and CamiSu), there's a similar song in Oz (and thus much later than the ones Malcolm gave) called "The young man from Kiandra". Kiandra was a gold town in the Australian Alps and is known as the location of the world's oldest ski club.

It's sung to a slow 3/4 rhythm and has been used as a lullaby but seems to have no hostile intent towards the baby, nor any reference to chattels; more a reflective (and self-pitying) lament on the theme of "marry in haste and repent at leisure.

The first verse is as follows; I'll try and dig up the rest (another three verses and same chorus) later.

I am a young man from the town of Kiandra,
I married a young woman to comfort my home.
She goes out and she leaves me and cruelly deceives me
and leaves me with a baby that's none of my own.

Ch.
Oh dear, rue the day ever I married,
How I do wish I were single again.
She goes out and she leaves me and cruelly deceives me
and leaves me with a baby that's none of my own.

Cheers, Rowan