Sorry, I can't help with chords. But, for those who are interested, I found 2 recordings on Spotify:

WHERE THE MULCHAIR RIVER FLOWS, performed by ULC on "Spring" (2000)

WHERE THE MULKERE RIVER FLOWS, performed by John Beag on "Tá an Workhouse Lán" (2010)
https://www.youtube.com/watch?v=9JceLhJuVmo

ULC is a Denmark-based trio consisting of Peter Uhrbrand, Sonnich Lydom, and Seamus Cahill. The record label is Danish and most of the songs on the album have Danish titles. What you hear on that cut is a fine male voice (Cahill, if I had to guess) accompanied by piano and guitar. There is a review of the album at CDRoots.com and a detailed description with sound samples at AlbumTrad.com