My father used to sing this song to me and my brothers when we were small. I think he learned it in the army. I too only remember snippets of the lyric but what I do remember is a slight variation on these existing threads.

Two convicts were seated, within a prison cell.
Said one unto the other my life story I will tell.

(Don't remember the next line)
I had a wife, a lovely wife, and a little baby too.

One night when I came home after working hard all day
I found the fire it had gone out, my wife had run away

It was then I took to drinking what else was I to do?
I mixed with bad company and became a burglar too.

One night as I set out to rob a mansion grand.
I had my tools laid at my side and my revolver in my hand

As I crept through the window a gentle voice I heard
I fired one shot then cried aloud "my god I've shot my child.

Not a friend in all this wide world to tell my troubles to.
Nowhere to rest my weary head but within this prison cell.

I have racked my brain trying to remember more of it and perhaps I have subconsciously borrowed from other versions on this thread but this song has stuck with me all my life. My mum hated it. She used to say dad was being morbid if he sang it.
My dad was born in 1912. I don't think he would have heard a lot of American music at that time so I suspect the song is English in origin.