I've parked on Buckingham St which isn't too far from Connolly Station in the past, both on working days and Croke Park Sundays - parking is free and never had a problem with security, etc. I've used the part of the street closest to Amiens St rather than further up, nearer Summerhill which I think has double yellow lines anyway.
If you are heading in towards the city via North Strand / Amiens St, Buckingham St is the right turn just before you go under the railway bridge.