I did search through the Hawaii State Vital Statistics Collections and another favorite database of mine Papakilo run by OHA for Medeiros family. No luck with my direct ancestors.
The lady whose been running the Portuguese Hawaiian Genealogy and HeritageWeb Site since 2001 which had a link to this research guide and also a list of genealogical aids for researching Azores ancestry and also runs her separate blog where she documents her Portuguese ancestry research, said that looking for records of church's in the area our ancestors lived would be a good idea.
My tutu says her dad's side was Catholic. (Which makes sense, obviously.) And that she herself was baptized in the Catholic church (which does so very early) though her mother was a staunch Mormon and she was baptized a member of the Church of Jesus Christ of Latter Day Saints when she became of age. (We don't baptize children until they are at least 8 in the hopes that they understand the covenant.)
Anyway, I found a site that said St. Raphael's church in Koloa is the oldest on the island, so maybe when I go home next I will pay them a visit. Of course, what I need to do is talk to my Portuguese family still living. (Who my father has the contact information for.) Take my own advice I give when teaching, collaboration brings the richest rewards.