I have a copy of Ray A. Jones "Ulster Pedigrees. Descendants, in Many Lines, of James Orr and Janet McClement, who emigrated from Scotland to Northern Ireland ca 1607". It's an updated book version of the Orr Pedigrees MS in the Linen Hall library in Belfast, and hundreds of surnames are mentioned in it.
The earliest Minnis in the book is Rosanna Minnis who married Thomas Orr junior and they moved to Scotland. No dates given but seems to be late 1700s.
The next Minnis in the book is William Minnis of Lisdoonan who married Eleanor Orr. They had 11 children - David, Samuel (both went to America), Eleanor (married an Irvine), William jnr. (married Jane Warren), Agnes (married John Galbreath), John (married Mary Magee), Mary (m. Robert McGibbon), William (m. Margaret Patterson), Francis, surgeon (to America), Lydia, Grace (m. Wm. Martin).
There's nothing about later Minnises but I know that the surname is still found in NE Down and last century when I was researching my Co. Down ancestors I corresponded with a lady called Minnis who was an office-bearer in the Saintfield Heritage Society. She sent me some of their journals with interesting articles, and one of them had an article about Francis Hugh Campbell Morgan Minnis (1912-1985), a local man who became a scientist and worked on radar in WWII.
Harry
PS Niblock is not a common name here but back in about 1965 when I was a student in Edinburgh I lodged briefly with a couple called Niblock. Mike Niblock was a sub-editor on the Scotsman newspaper.