How lovely that you will come and explore the island of Ireland on a self-driving adventure! Which places do you plan to visit? I understand you have already done quite a bit of research for your trip, that's great. I'm happy to provide some information regarding your parking question.
This Community forum thread explains a bit more about parking in Ireland
. As you can see there is no one app that will allow you to pay for parking across the island as it is managed at council level. On the Citizens Information website you can find more information about traffic and parking
Depending on where you are planning to go, I will be happy to check if there are apps that you could use.
Note also that some apps may not be available while you are in Canada due to potential location restrictions.