While doing some research on this song, I found this thread. I first heard it on the album The Weavers' Almanac. There's no date on my old vinyl copy, but it's obviously from the early 1960's, having been released after The Weavers at Carnegie Hall - Vol. 2. (One Internet source says 1963, but I can't verify that.) At the time, The Weavers were Lee Hays, Fred Hellerman, Ronnie Gilbert and Erik Darling.

From Studs Terkel's liner notes:

WHEN THE STARS BEGIN TO FALL - The theme of resurrection has always been part of the substance of Western music. This is what may be described as a jubilee song, in contrast to the more somber spirituals. It has the elements of belief and hope everlasting. These great old songs have a way of staying around and popping up when they are needed most, and end up being as timely as today's or tomorrow's newspaper.

Here are the words, exactly as transcribed from the record:

My Lord, what a morning
My Lord, what a morning
My Lord, what a morning
When the stars begin to fall

Oh sinner, what will you do?
Oh sinner, what will you do?
Oh sinner, what will you do?
When the stars begin to fall

You'll weep for the rocks and mountains
You'll weep for the rocks and mountains
You'll weep for the rocks and the mountains
When the stars begin to fall

My Lord, what a morning
My Lord, what a morning
My Lord, what a morning
When the stars begin to fall

Oh, who will hear the shout of victory?
Who will hear the shout of victory?
Who will hear the shout of victory?
When the stars begin to fall

Will there be time to find salvation?
Will there be time to find salvation?
Will there be time to find salvation?
When the stars begin to fall

My Lord, what a morning
My Lord, what a morning
My Lord, what a morning
When the stars begin to fall
When the stars begin to fall

Nearly identical to what has been posted above, and probably predates the version by The Seekers (which I've not yet heard). What I find interesting is the credits say: Additional words, arr. & adpt. Hays, Hellerman, Gilbert, Darling. So, perhaps this particular version owes much of its lyrics to The Weavers.

Jay