On the original handwritten Baptisms of John and Daniel (from LDS IGI) the original name of the father Robert has been changed from what looked like Bodoagh to Boyd.
So found the marriage of Robert Boddaugh to Margery Corlet , 28/8/1763 in Parish of Ballaugh, Robert was a widower and from that Parish, Margery a spinster for Lezayre.
There are births for Robert Boddaugh and Phillip Boddaugh in 1763, but mother is shown as Mary, original documents in poor condition, so cannot be checked.

Plenty of deaths on Brian Lawsons site for Boddaugh up to the 1700's early 1800's , but by the 1841 census the name has disappeared , only Boyd and Boyde.
Cheers
David Dwyer