Looking for Keenan Frederick of New Zealand

I am trying to locate any records in New Zealand for my great grandfather Frederick Keenan.
I have a letter written by him stating that he was born in Wellington, New Zealand july 24 1876 and that his parents died when he was very young.
He grew up in an orphanage and then left New Zealand at the age of about 18 on a merchant marine ship.
So far I have not been able to find his birth record and do not know which orphanage he was located in.
He possibly had a brother named Frank. I do not have his parents names.
He became a U.S. Citizen in 1905 and resided in Kitsap county, Washington.
Any advice as to how to search for his orphanage/school records would be very helpful.