The Irish surname CANNON has three origins in Ireland:
Ó Cannanáin of Tirconnell, is one of the most ancient, if not the most ancient, of hereditary surnames recorded in the Annals of the Four Masters (AD942/3), in the person of Ruadri Ua Cannanáin. This surname is no doubt the source of many Donegal CANNONS.
Ó Canáin, a distinct surname from the above, belonged to the Uí Maine and also became anglicised as CANNON, and would, therefore, appear to account for the majority of the Connacht bearers. A possible conjectural root is 'cano' - a wolf-cub (Woulfe).
The English surname CANNON from Old French ‘canoine (canon)’, an ecclesiastical office, is also present in Ireland due to immigration either from Anglo-Norman settlers, post Elizabethan English settlers and Huguenot refugees.
In the 1847-64 Valuation of Ireland by Sir Richard Griffith most CANNON households were to be found in Donegal (201), Leitrim (79), Mayo (77) and Galway (75).
In the 1890 Birth Index most CANNON births were registered in Donegal, Leitrim and Mayo.
Both records indicate that the majority of Irish CANNONS would be from the two above native Irish origins.
As for the arms here illustrated, they appear in Burke's General Armory, 1884, under the variant CANON, with no reference to any Irish connection in that text. The only other arms, quite different, with an Irish connection mentioned in that work is a funeral entail in Dublin of a family with similar arms to those of Scottish CANNONS.
1847-64 Valuation of Ireland, Sir Richard Griffith.
1890 Birth Index, from Special Report on Irish Surnames, Robert E. Matheson, Registrar General, 1901
Sloinnte Gaedheal is Gall, P. Woulfe, Dublin 1923
Irish Families series, Dr Edward MacLysaght, Irish Academic Press, Dublin, 1982/5