I have been contacted recently by a gentleman who is doing some fine research into the Irish dialect of Dublin, now extinct.
He contacted me as the result of work I do highlighting East Ulster Irish and Kilkenny Irish.
I know little of the Gaelic dialect of Dublin though I would be very interested in finding out.
Although I fear one may never get a definitive answer to this question and that it could produce unnecessary wrangling without real result as has battered the Cornish language movement.
I think the most important aspect of study into Dublin Irish may not be the precise nature of its vowels and consonants but perhaps the fact that it could educate people as to how late the dialect was spoken and by whom.
Dublin Irish survived well into the 19th century but is not recorded nor transcribed phonetically but of course historical linguistics (based on isoglosses and place-names historical forms) may be able to lay down the fundamentals.
We have recordings of Louth and Kilkenny Irish and have a lot of material from Meath, Louth (including Drogheda) and from Kilkenny. We also have some (modern) Gaelic material from Wexford, Westmeath, Kildare if only snippets.
Close study of this archive may be vital.
These are the important sources for those trying to piece the clues together :
Labhrann Laighnigh by the late Daithí Ó hÓgáin.
Piatt, Donn S.: “Gaedhilg na Midhe”, An tUltach 14:7 (8/1937) 5 (Tomás Mac Eochagáin).
Piatt, Donn S.:
____: “Giotaí de Ghaeilg dhúchasach na Midhe”, An tUltach 29:6 (6/1952) 11-12.
Laoide, Seosamh: “The Leinster dialect”, An Claidheamh Soluis 12:40 (10/12/1910) 21; 12:43 (31/12/1910) 5-6; 12:48 (4/2/1911) 5-6.
Piatt, Donn S.: Gaelic Dialects of Leinster (1933) (inc. South Dublin, Wicklow, Kildare, Laois, Offaly, North and West Wexford, Kilkenny, Carlow; North Dublin, Westmeath).
Piatt [Ps. Laighneach]: “Áth Cliath is Cill Mhanntain”, An tUltach 10:5 () 6; 10:7 () 4.
Piatt “Gaeilge na Mí”, An tUltach 44:9 (9/1967) 9-10.
Williams, N J A: “The Irish language in County Offaly”, Offaly: history and society (c1999).
Williams (Nicholas): Gaeilge na hIarmhí.
In Féilscríbhinn do Chathal Ó Háinle (2012), pp. 1009–1058.
Includes a Liosta focal (Irish-English) of words likely to have been used in Westmeath Irish.
Williams (N. J. A.): Téacsanna foghrúla ó Chontae na Mí.
In SHib 31 (2000–2001), pp. 277–291.
Based on material collected by Seosamh Ó Laoide (1865-1939) from native speakers from Moynalty (Lower Kells) and Somerville (Upper Slane).
And of course …
Williams (Nicholas): Na canúintí a theacht chun solais.
In SnaG (1994), pp. 447–478.
On a personal note I have not the slightest doubt the Irish still spoken in Mayo would be the most similar to that once spoken in Dublin though I would not be prepared to contest that assertion as it is not important to be personally.
However I would study carefully the Irish of Omeath and Kilkenny to set the dialect in its proper place in the continuum.
I would also suspect that given Dublin’s status as a port and as a Viking settlement in its history that is may well have be influenced by Munster Irish more than the surrounding dialects and I suspect it would have had many similarities to Manx.