Looking for O'Sullivan/Mcenerney? family

Hi, my name is Annie Molloy and I have been searching for nearly 15 years to find my great grandfather's parents who were James? Sullivan (circa 1820)who was married to Honoria McInerney? (circa 1825 )(many spelling variations I have found out :) ).

Their son Micheal Joseph Sullivan was born in Limerick either 1850 or 1859 as he has given two different dates on his marriage certificate and his wife Ellen Caples from Conna in Waterford put 1859 on his death cert.

He arrived in NZ (Hawkes Bay) in 1878 from I am not sure but presuming Ireland.

I have just received his last will and his daughters have stated that he had English citizenship as his parents were Irish but lived or were residents in England. Very confusing as he states he was born in Limerick in all docs that I have seen.

This is all I have and he named his firstborn son James so I am hoping that the name James for Michaels dad is correct and he could be Jerry Jeramiah etc :)

I hope this finds you all well and happy and if anyone has any thoughts on this or how to go about finding out more I would love to hear as all of the big repositories do not seem to have them anywhere. I have found a family in Abbeyfeale that may be a link and that is why I am posting here.

Kind regards from the antipodes Anne