OK, an update to my last post, Aer Arann do have mode S fitted, but they do not transmit the full ADS-B information, so they will not appear on the map. Also, as they don't display a Flight ID, you won't be able to search for them in MyLog. However, if you look to see if you have received any on the company registrations, or use the filters in MyLog to look for Airline = Aer Arann (use the drop down for the airline) they should be there.
Registration Manuf. Model Type c/n l/n Reg/Opr built delivery until status
EI-BYO ATR ATR 42-300 AT43 161 REA 1989 2002-12-20 active
EI-CBK ATR ATR 42-300 AT43 199 REA 1990 1998-12-24 active
EI-CPT ATR ATR-42-300 AT43 191 REA active
EI-CVR ATR ATR 42-300 AT43 022 REA 1986 2001-01-17 active
EI-CVS ATR ATR 42-300 AT43 033 REA 1986 2001-03-16 active
EI-REA ATR ATR 72-202 AT72 441 REA 1995 2002-05-30 active
EI-REB ATR ATR 72-202 AT72 470 REA 1996 2002-05-17 active
EI-REE ATR ATR 72-202 AT72 342 REA 1992 2003-12-10 active
EI-REF ATR ATR 72-202 AT72 201 REA 1990 2004-06-18 active
EI-REH ATR ATR 72-201 AT72 260 REA 1991 2005-09 active
EI-REI ATR ATR 72-202 AT72 267 REA 1991 2005-11-18 active
EI-REJ ATR ATR 72-201 AT72 126 REA 1989 2006-05-20 active
EI-REL ATR ATR 72-212A AT72 748 REA 2007 2007-05-25 active
EI-REM ATR ATR 72-212A AT72 760 REA 2007 2007-10-25 active
EI-REO ATR ATR 72-212A AT72 787 REA 2008 2008-08-12 active
EI-REP ATR ATR 72-212A AT72 797 REA 2008 2008-08-12 active