From Tim Davis's site, he also has the parents of William QUAYLE (m Catherine MYLREA) as John Quayle & Margaret Quayle. However, he suggests that this John was baptized 1 Sep 1736 at Kirk Michael, son of John QUAYLE (bp 1 Feb 1690/1 KK Michael, bd 24 Jan 1746/7 KK Braddan) and Joney CORLETT (bp 10 Dec 1697 KK Lezayre, bd 7 Jan 1778 KK Michael). John & Joney were married 29 Apr 1718 KK Michael.
I don't know which is right: the John bp 1731 son of William QUAYLE & Isabel CORLETT or the John bp 1736 son of John QUAYLE & Joney CORLETT. Does anybody else know for sure?
Going one generation further, Tim Davis has the parents of John as John QUAYLE (bp 17 Jan 1652.3 KK Michael son of Dan QUAYLE) and Ellinor CORJEAGE (bd 5 Mar 1722/3 KK Michael), who married 23 Jul 1671 KK Michael.
On Tim's website, Joney CORLETT's father was Jon CORLETT.
Margaret QUAYLE (who married John QUAYLE) was baptized 7 Oct 1733 dau of William QUAYLE and Margaret CAINE. This latter couple are my ancestors via son David and grandaughter Judith (Joney). So far, I don't know who the parents of William are, but Margaret was the daughter of William CAINE & Elinor.