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.