Try here (from the MMC website - European dealers)? Some UK dealers have cars for rental, perhaps the Irish dealer will too.

Morgan Cars Ireland
Red Cow House
Red Cow
Naas Road
Dublin 22
Ireland

mobile: 00353 1 4642211
email: jeff@harley.ie

There's an article here:
http://www.irishtimes.com/newspaper/motors/2008/1105/1225523368411.html

Or alternatively why not try the Lake District (Cumbria, UK) - it's a great area for a Morgan - where you can hire a Mog and accommodation:
http://www.lakesanddales.co.uk/classicca...-drive-a-morgan

There doesn't seem to be a Morgan owners' club in Eire but perhaps someone from the MSCC in the UK could advise.

Enjoy your holiday