Hi Aideen
The problem is the ring suspension on the first medal (nearest the heart). This is not for a campaign (unless you go back to the Turkish Crimea), but more likely for a royal visit, jubilee etc. Either way he is wearing them the wrong way around, as it was campaign medals first, then commemorative.
The Connaught Rangers had green facings (collars and cuffs) while all other Irish Regiments were 'Royal' and had royal blue facings. So no help there.
The Connaughts did wear two types of collar badge - a Irish harp with a scroll underneath and an elephant (without a howdah). And he could be wearing both. Or he has his collar undone. So a better scan of the collar badges is also needed. Their museum may be able to tell you if they wore them together at any time.
The cuffs for the Regulars were cut straight across until c1901 and for 20 years before. And I believe they also lost the white front piping. So I would guess he is in the Militia, after serving as a Regular when he received both campaign medals at least.
Ancestry have 19th century medal rolls, and Findmypast have surviving records for the Regulars and Militia.
The Connaught's Militia were separate regiments for Galway, Mayo and Roscommon. They were also the county regiment for Leitrim, but the Leitrim Militia were affiliated to the Rifle Brigade. Men had to live in the county to be in the Militia. So that should be a clue.
They were formed in 1881 from the 88th and 94th Regiments of Foot, and these titles were still being used well after 1881.
Ken