While Cork isn't the biggest city in the world (or Ireland), you'd really need to provide a little more detail.
Are you staying in the city centre? If so, which part of the city? Which direction are you coming from/going to?
Lots of on street parking available which will be free, as long as you're able to move it fairly early in the morning. If staying in a Hotel, some will reserve a place in their car park if notified in advance.