The Database of Vital Statistics from New Brunswick Newspapers is available on the Provincial Archives of New Brunswick website. The database contains genealogical extractions from New Brunswick newspapers from 1784-1896 and can be searched at the Provincial website. It might have been there for a while, but today was the first time I noticed it. My Neills were in New Brunswick for a short time so I was glad to see it online.
It is wonderful source. Read the background and what it contains before you search.
