Actually the morgue is the small building behind the Coroners Court which is probably the fine little building you're thinking of. From The Irish Times:
The old City Morgue was designed by the then City Architect, Charles J. McCarthy, in 1901. Mr McCarthy went on a fact-finding tour of English coroners' courts with the chairman of the Corporation Finance Committee, Councillor Joseph Nanetti, who is mentioned in Ulysses.
The morgue was built on the site of the old Custom House flour mills. It cost Â£4,504. The building it replaced became part of the original Abbey Theatre.
The morgue has been featured in a number of novels. Patricia Cornwell, who visited it to research her novel Unnatural Exposure, describes some of the fittings as being suitable for a "medical museum". It also features in Paul Carson's novel Scalpel.