Kytrad, thank you for your kind and informative reply. Stars seems more logical to me than star's (but I can't argue the point, except to mention the Stanley Bros., the Seegers and others who sing or have sung Appalachian songs use the plural).
Since this is a 'folk' song I can't argue with either 'bright morning stars are shining,' or '...rising,' but the former, to me, fits better.

I don't think the original question by Erick can be answered yet, but perhaps more will be found.