There are a few rental companies mentioned in but unfortunately none of them apply to Ireland. Perhaps some of the companies mentioned therein operate in Ireland also.
I have heard that Enterprise are quite good but have not used them myself.
Enterprise is certainly a good bet (especially at the weekends - maybe not so good for longer periods ?) - Try [broken link removed] can have good deals sometimes (and would be a better bet than enterprise for pick up at the airport)
Do you really need an automatic ? - They are always (a lot) more expensive to rent - if you can get by with a Manual it will save you a good few quid.