With the amalgamations of 1881 facing colours were simplified. Royal regiments - royal blue; English and Welsh regiments - white; Scottish - yellow; Irish - green. Following some resistance by regiments who had longstanding facing colours with traditions behind them, over time many of these regiments regained their old facings. 'Jam-pot' cuff seen in the photo was introduced in 1881. There being also resistance to this, one later modification was to the sergeant's cuff to which a crowsfoot or knot was added. (Carman 'British Military Uniforms'p142). Thus the photo is later than 1881.
However, shoulder titles were used by other ranks for the first time on the khaki drill uniforms in India in 1885. 'Home service and other forms of dress at first had the title of the regiment stitched into the shoulder strap.' (Westlake 'Collecting Metal Shoulder Titles' p1). I think theres a good chnace that work on the photo with something like Photoshop might resolve this title to SWB. There are also collar-dogs present but I don't have information on these.
The flag of St. George seems to make no difference since their is a clear picture of an SWB man with identical badging in Regiment magazine #43 p 40 of which the caption claims it dates to 1885. However in that picture the knot referred to above is absent form the cuff so it would seem the SWB's fight to have this addition didn't succeed until after that date.
The regiments website places the 1st Battalion in Ireland as follows:
*26 September 1883 - September 1885 Kilkenny, Ireland (detachments at Killarney, Waterford and Duncannon)
September 1885 - October 1886 Curragh Camp, Ireland
October 1886 - September 1887 Birr, Ireland
September 1887 - December 1889 Dublin, Ireland, (in camp Phoenix Park August - October 1889), Balls Bridge, November 1889*
I would say therefore that your man is a SWB and the photograph dates 1885-1890.
You will find some helpful information on further research at the Royal Regiment of Wales (24th/41st) Museum website
http://www.rrw.org.uk/ They will probably be willing to identify the uniform fully if you send a scan to them.
But you will need to establish his first name to get anywhere. Also you may not have any luck with the 1881/91 censuses since these were not preserved for Ireland which is where they were quite probably living on these census dates.