Grattan, clearly you don't remember the old Willy and Joe cartoon. But I think an Irish army is a valid choice. There was an Irish army in period, so it could have fought, and a lot of miniature warfare consists of "what ifs."
Hypothetical One: Britain decides to seize at least the ports they were promised use of in future wartime in the treaty creating the free state, to protect ships from U-boats. This actually got to the planning stages very briefly in 1940. Presumably British vs Irish with the possibility of air-dropped or submarine-delivered German weapons for the Irish.
Hypothetical Two: Germany settles on a "back door" approach to an invasion of the UK, and lands troops in Ireland by air or (perhaps) sea, hoping to bring Ireland into the Axis. In this case the Irish army might fight on either or both sides, and British intervention would be a possibility.
Hypothetical Three: The free state agrees to join the Allies in return for Ulster. This was actually proposed by de Valera. In that case, feel free to add Irish units to Dieppe, Alamein or D-Day, possibly with some American or British equipment.
Hypothetical Four: The easy one. Small groups of clandestine forces--SOE, Brandenburgers, what have you--enter Ireland for any number of reasons--to take out particular assets, free prisoners or provoke Ireland into entering the war in a "false flag" attack. The Garda and the Irish Army have to prevent this.
I don't do any of these. But I'm wargaming in Indiana. If I were wargaming in County Cork, I'd almost surely have troops and terrain for 1919-21, and adding the necessary for Hypothetical Four would be very tempting.
