I've now made searches as I said I would; all is negative.

The assertion is that the Fields of Athenry was printed in 1888 in Dublin by someone called Devlin.

1. There is nobody of the name Devlin listed among:
Printers (letterpress or photolithographic)
publishers
booksellers
Music Sellers
musical instument makers or dealers
music and pianoforte warehouses
print sellers
in the city or county of Dublin in Thom's Directory for 1887, 1888 or 1889

2. The catalogues of the two major collections of Irish Books made in the 19th Century - Bradshaw and Gilbert have no printer or publisher of that name listed.

3. There is no Devlin given in John A Parkinson: Victorian Music Publishers (Harmonie Park Press, Michigan, 1990) (Detroit studies in music bibliography no 64) which used the catalogues of the British Library, the National Libraries of Ireland, Scotland and Wales, the University Libraries of Oxford and Cambridge and also used the annual Musical Directory (1853 - 1931).

It is agreed that this is not conclusive but it does reduce the likelihood that the assertion is true. I now believe that it is up to those making the assertion to justify it.