Hmm - that's a clever idea. Let me think....
"Morning Has Broken" (best-known by the Cat Stevens recording)
"Morningtown Ride" (written by Malvina Reynolds)
"Sunrise, Sunset" (from Fiddler on the Roof)
"Try to Remember" (from The Fantasticks)
"Chim Chim Cheree" or "Feed the Birds" (from Mary Poppins)
As you see, my brain seems to be channeling musicals this morning along with the classic folk, but that may at least get you started.