Hello Donna!
Thanks for posting!
Your cousin can look into private chauffeur services, of which there's a
list available here. You can also find professional private drivers and chauffeur services listed in the
Transport & Getting Around section, where you'll see a range of options. In addition, you may find it helpful to browse other
community threads where fellow travellers have shared first-hand recommendations for reliable drivers they've used in the past.
Alternatively, there are direct bus connections between Cork and Ardgroom (bus to Harrington's Ardgroom 231, leaving from University Hospital, Cork), which takes about 2h20. Routes can be checked on
Transport for Ireland or
Rome2Rio.
Hoping that helps!
Alex