song is in standard tuning, the way i hear it christy uses chordvariations while
fingerpicking the song.
anyway, an easy overview over the chords used:

     G (320003@1)   C (x32010@1)   F (133211@1)   AmE    3     x     x     x
A (x02220@1)  x     3     x     0
D (xx0232@1)  0     2     3     2
G (320003@1)  0     0     2     2
B (x2444x@1)  3     1     1     1
e (022000@1)  3     3     3     0

christy uses some variations on the high e-string and on the rute notes to make 
the song softer. i didnt figure them out, but i'm sure you can by just trying. ah 
and the song's in 3/4!


G (320003@1)                C (x32010@1)           F (133211@1)        G (320003@1)You may travel far far from your own native home
     C (x32010@1)                         G (320003@1)          AmFar (x02210@1)away o'er the mountains far away o'er the foam
       C (x32010@1)                      G (320003@1)       AmBut (x02210@1)of all the fine places that I've ever seen,
        C (x32010@1)                      F (133211@1)          GThere's (320003@1)none to compare with The Cliffs of Dooneen

G (320003@1)                 C (x32010@1)         F (133211@1)               G (320003@1)Take a view o'er the water fine sights you'll see there
               C (x32010@1)                      G (320003@1)           AmYou'll (x02210@1)see the high rocky slopes on the West coast of Clare
    C (x32010@1)                 G (320003@1)            AmThe (x02210@1)towns of Kilkee and Kilrush can be seen
         C (x32010@1)                      F (133211@1)          GFrom (320003@1)the high rocky slopes at The Cliffs of Dooneen

G (320003@1)                  C (x32010@1)     F (133211@1)           GIt's (320003@1)a nice place to be on a fine Summer's day
         C (x32010@1)                       G (320003@1)      AmWatching (x02210@1)all the wild flowers that ne'er do decay
    C (x32010@1)                         G (320003@1)         AmThe (x02210@1)hare and lofty pheasant are plain to be seen
       C (x32010@1)                             F (133211@1)          GMaking (320003@1)homes for their young round The Cliffs of Dooneen

G (320003@1)                  C (x32010@1)            F (133211@1)        GFare (320003@1)thee well to Dooneen fare thee well for a while
       C (x32010@1)                     G (320003@1)       AmAnd (x02210@1)to all the fine people I'm leaving behind
       C (x32010@1)                           G (320003@1)         AmTo (x02210@1)the streams and the meadows where late I have been
        C (x32010@1)                      F (133211@1)          GAnd (320003@1)the high rocky slopes of The Cliffs of Dooneen


have fun with that great song :)