The answer to the question is kind of complicated.
There are currently 5 distilleries making spirit destined to become whiskey. These are Midleton, Bushmills, Cooley, Kilbeggan and Dingle.
However at present you can only buy whiskey from the first three on the open market, kilbeggan have a single malt at Dublin airport only and Dingle having just started will not have legal whiskey until just under three year's time.
To clarify there are blended whiskeys labelled as Kilbeggan also but these are all from Cooley.
There are currently plans to build another 9-10 distilleries in Ireland. The next will be Alltech's plant in Carlow (affiliated with Carlow brewing.)
West Cork Distillers are a bit of an odd operation. Kennedys was initially labelled as Irish Whiskey (or at the labelling inplied that). I heard that they ran into trouble with BordBia over the product and had to change it.