score:17
30 May, 1969.
Here is a copy of an obit published in the Desert Sun, Volume 42, Number 256, 30 May 1969
This information is confirmed by multiple other posted obituaries in the genealogical source, GenealogyBank Historical Newspaper Obituaries, 1815-2011. This is indexed at the FamilySearch.org genealogy site (signup probably required, but no fees):
Robert Briscoe Principal
Birth about 1895
Death 30 May 1969 Dublin, Ireland
Obituary 31 May 1969 San Francisco, San Francisco, California, United States
Other Fianna Elreann
Robert Briscoe Principal
Birth about 1895
Death about 30 May 1969
Obituary 30 May 1969 Seattle, King, Washington, United States
Lord Robert Briscoe Principal
Birth about 1895
Death 30 May 1969
Obituary 31 May 1969 Jersey City, Hudson, New Jersey, United States
Other Hudson J Strong
Lord Robert Briscoe Principal
Birth about 1895
Death 30 May 1969
Obituary 31 May 1969 Jersey City, Hudson, New Jersey, United States
Other President Eamon De Valera, Valera Briscoe
Robert Larkin Briscoe Principal
Birth about 1895
Death about 30 May 1969 Dublin, Ireland
Obituary 30 May 1969 Washington, United States
Father Bob Briscoe
Other President Eamon De Valera, Denis Larkin
Note the entries which say about 30 May 1969 are following the genealogical procedure used when a date isn't stated directly in the obituary being indexed.
The original obit posted mentioned he died peacefully during the night. Without a death certificate it may be impossible to tell if he died before or after midnight. This might explain the entries which are listing May 29, they are reading it as died last night indicating the night of the 29th. It is when the death is reported on the 30th, (news of the death hit Dublin at breakfast time) that is what is being recorded in most of these sources.
So obituaries published in Palm Springs, San Francisco, Seattle, Jersey City, and Washington all agree that Robert Briscoe died 30 May, 1969.
User @Andrew posted a comment indicating further agreement in articles from Belfast and Liverpool. (signup required/ pay service)