My project is an Android travel app with Irish map and POIs.
Where can I find free sources with Irish POIs?
You could use data from OpenStreetMap (OSM).
From the OSM webpage: "OpenStreetMap is open data: you are free to use it for any purpose as long as you credit OpenStreetMap and its contributors. If you alter or build upon the data in certain ways, you may distribute the result only under the same licence." (http://www.openstreetmap.org/about)
Here is some information about using OSM in Android apps: https://wiki.openstreetmap.org/wiki/Android#Libraries_for_developers