The IRA isn't a single, unitary organization, and has often been divided by factionalism (e.g., Real IRA, Continuity IRA, Provisional IRA, Original IRA, etc.). Thus, they don't have an email. Not to mention that posting an "official" email address would not fare them well, as those can be easily monitored, their access points traced, and this can ultimately lead to the capture of their members.
Irish Republican Brotherhood was created in 1858.
Irish Socialist Republican Party was created in 1896.
Provisional Irish Republican Army was created in 1969.
Stephen Hayes - Irish republican - was born in 1902.
Stephen Hayes - Irish republican - died in 1974.
Jim McAllister - Irish republican - was born in 1944.
Dissident Irish Republican campaign happened in 1998.
Sean Kelly - Irish republican - was born in 1972.
Gerard Casey - Irish republican - died in 1989.
Thomas Bryan - Irish republican - was born in 1897.
Patrick Maher - Irish republican - was born in 1889.
Brian Keenan - Irish republican - was born in 1942.