Bold Riley (the way Kate Rusby does it, which I know is anathema to chanty singers but is gorgeous just the same)
Soon One Morning (Old spiritual and great to get the audience involved in trying some harmonies)
The Great Storm is Over (old gospel, and ditto)

Meanwhile, I'm printing out this thread as well for some of the suggestions I can try. I've been thinking that I need to expand my unacompanied repertory (there's an old thread lying around here somewhere on the difference between unaccompanied and a cappella, and it convinced me to stop callingi t a cappella and start saying I sing unaccompanied.)

And as a singer, I can tell you, in answer to Mac Tattie's question above, that I enjoy finding my own material but am always pleased when someone else shoves a beautiful song in my hand and says, "Here, you simply must try this one on for size."

Some of them do, some of them don't,but it's always nice to have the selection from which to choose.

Good luck to both of you, WW