I'd say you'd be pushing it. You'll land maybe a bit early, but you've got to taxi to the gate, wait for the door to open, wait for a plane full of people to be herded off. If you're collecting bags, there's another wait for the bags to wander their way from the plane to the baggage belt. I'd say all that is a minimum of 30 minutes from landing time to Stamp My Passport time.
Immigration/Passport control can take anywhere from 15 minutes to 60 minutes depending on which travel gods have been prayed to that day. Then there's the journey to the train station which will take about 45 minutes according to Rome2Rio. Once at the station, you'll have to collect your wits after all that rushing to figure out which platform you need, and then get to the platform.
So, with all that, I can't imagine having enough time unless you are incredibly lucky.
Another option besides the train (which looks like it only runs once daily to Killarney), is to hop the bus (Dublin Coach 750 or 726) at the airport to what's called the Red Cow Luas station (an easy and comfy 20 minute ride). From there, there's an hourly bus (Dublin Coach 300) to Killarney. You can look up your options at https://www.transportforireland.ie