I listened to the excerpt and I was able to transcribe this much, for what it's worth:

"There's a spot that I love dearest
Sure I think I see it still.
It's that little town in County Down,
Rathfriland on the Hill.

Sure its brow is decked with em'ralds
Wild flowers around it grow.
When the sun does shine, it looks so fine
All in the …"

Also, I learned that "Rathfriland on the Hill" was recorded by Ruby Murray on her LP, "This Is Ireland," Fontana TL5444.