I guess you are a daughter of Beth W. Your cousin Paula A. + I did most of the Quine genealogy which is on the Family Search database.

The William Quine you mention is the son of Silvester Quine of Ballig, Onchan, and Silvester is the son of Thomas Quine of Kenaa, German.
I still have no origins for the Quines of Kenaa.

The Gilnoo mentioned by me seems to be of the Strenaby lot, as I cannot fit him into Arderry.