Correct me if I'm wrong. There has never been an Irish Astronaut. Ireland contributes to the ESA, there have been Astronauts from many other European nations. U.K. is sending their first sole-citizen into space soon. I would love to seen an Irish Citizen go into Space.
Helen Sharman appears to have escaped your notice. She was British.
The government didn't pay for it, but she was still the first British citizen in space.
Also, the Irish don't really contribute anything to ESA. There's no major research done there, no major funding and no real interest in human spaceflight. Therefore there's no reason to allow them an astronaut slot.
(edit) And before anyone says that the UK has no interest in spaceflight: That's true, but they still contribute large amounts of money and research to the cause, particularly through Astrium.