According to Songs of America and Homeland the music is by M. W. Balfe (1808-1870).

By Killarney's lakes and fells,
Em'rald isles and winding bays;
Mountain paths and woodland dells,
Mem'ry ever fondly strays.
Bounteous nature loves all lands
Beauty wonders ev'rywhere;
Footprints leaves on many strand,
But her home is surely there!
Angels fold their wings and rest,
In that Eden of the West
Beauty's home Killarney,
Ever fair Killarney.

No place else can charm the eye,
With such bright and varied tints,
Ev'ry rock that you pass by,
Verdure broiders or besprints.
Virgin there the green grass grows,
Ev'ry morn Spring's natal day;
Brighthued berries daff the snows,
Smiling winter's frown away.
Angels often pausing there,
Doubt if Eden were more fair,
Beauty's home Killarney,
Ever fair Killarney.

Music there for Echo dwells,
Makes each sound a Harmony,
Many-voiced the chorus swells
Till it faints in ecstasy.
With the charmful tints below
Seems the Heaven above to vie,
All rich colours that we know,
Tinge the cloud-wreaths in that sky.
Wings of Angels so might shine,
Glancing back soft light divine,
Beauty's home Killarney,
Ever fair Killarney.

I have a midi of it at Killarney (http://www.contemplator.com/folk6/kilarney.html) - except that this morning my ISP is not working!!! Argh! Well, I need a cheaper host anyway... guess I'll start looking!