Monday 2 May will be a public holiday in both the Republic of Ireland and Northern Ireland.
Excepting the National Library of Ireland (see below), all libraries and archives typically used by genealogists will be closed on both sides of the border. Branch libraries in the Republic may also be closed on the preceding Saturday. I'm not sure if the same happens in Northern Ireland (LibrariesNI's website doesn't provide any clues) but the Linen Hall Library in Belfast is open for normal Saturday hours: 9.30am - 4pm.
The National Library of Ireland will be open over the long weekend as follows:
Main Reading Room, Manuscript Reading Room and Readers Ticket Office – Kildare Street: open on Saturday 9:30am to 12:45pm. Closed Sunday and Monday.
Exhibitions (1. William Butler Yeats & 2. World War Ireland) at Kildare Street – open on Saturday 9:30am–4:45pm; on Sunday: 1pm–4:45pm; and on Monday 12pm–5pm.
National Photographic Archive Exhibition Galley in Temple Bar – open on Saturday 10am–5pm; on Sunday 12pm–5pm; and on Monday 12pm–5pm.
Genealogy Service, Café Joly and NPA Reading Room closed Saturday, Sunday and Monday.