Last fall I saw a pre-release film on Hazel Dickens. On in she sings an acappella version of How Tedious and Tasteless the Hours, that has to be related to the old Shape Note tune Green Fields. I asked about it being on CD, the answer was no. I've also seen this in old Methodist Hymnals.

The Bluegrass gospel "Beautiful Star of Bethlehem" might work acappella. "I will arise" is another old folk hymn that might work. I like the 'Wayfaring Stranger' suggestion as well.

Some old standards that might be Ok for bluegrass, but I'm not sure: 'Rock of Ages,' 'It is well with my soul,' 'Nearer, my God, to Thee.'