The version with the extra verse has been done by Roy Orbison, which I was lucky enough to borrow to add to my collection ( I now have 27 versions of Danny Boy) which no doubt you may realise has a very special meaning for me personally. (Thereby lies a long story over many years of my life), anyway I must say that Roy Orbisons version is the most poignant, heartbreaking version I have heard.

Whilst I don't know the author of the extra verses, it has been added to imply the return of Danny after many years to his fathers resting place, there is also a piece added onto the end.
Here are the words of Roy Orbisons version:-

The valley is hushed the flowers are all dying
The meadow is white with the winter snow
Lord as I stand at the place where daddy is lying
I say a silent prayer and somehow I know
He hears me there though soft I tread above him
So now he sleeps in peace his Danny boy's come home

(It then goes into the "normal" Danny Boy lyrics, then at the end, this)

I close my eyes and still I can see him standing there on the hill
Tears filled his eyes as he waved goodbye to me
I can't forget, I guess I never will
He said, the valley is hushed the flowers are all dying
The meadow is white with the winter snow
Come find the place where you know that I'll be lying
Say a silent prayer so I'll know.

Whew, never done so much typing, hope this helps.

Wilby