Hello Pascal,
How nice that your son is coming over to study here soon! First of all, I would recommend getting a regular Leap Card and loading it with tickets as needed. Here's an
overview of the tickets you can load on a Leap Card
There are monthly tickets for Dublin (Dublin Bus and Dart train). In order to travel around the island I would suggest topping up the Leap Card depending on your son's needs. (fares are also cheaper this way)
Furthermore, we have
a previous thread about the public transport passes as well as
additional info.
Talk soon,
Antoine