We will be landing at Shannon and immediately driving to Dublin. I would like to drop the car off outside Dublin to avoid driving in the city. Any suggestions for a train station with a safe car park that would be easy to access? The car would be there for 48 hours.
Maybe it won't work because of other things you are doing (stopping places en route to Dublin, a weekly rental rate vs a shorter term rate for your car, etc) but if it were me, I would just take the train to Dublin and rent a car when you are ready to leave the city. Parking is expensive, and you are paying for a rental that you aren't using plus a place to keep it. The easiest place to leave it, though, would be the airport, I think, then take the bus into town.
Leave it at the airport. Bus into the city center.