David
you are in the twilight years of the dominance of the established church, by late 1870s civil registration had become compulsory and the church's connection to punishing 'moral' failings (eg fornication etc) and the need for baptism to be admitted to church controlled schools or even to get married was about to be removed (tho marriage within a church rather than a civil ceremony allowed by law since 1840s was still the social norm until very recently) - more couples were not concerned to have children baptised, others baptised within their own group eg the Methodists and thus did not appear in any CofE registers (most of these Methodist registers are now held at Manx Museum); Roman Catholic numbers were increasing on Island.

You have also commented on typical Manx usage of 2 'Christian' names - the official 1st and the common use of the 2nd causing some confusion.

There may not be a baptism to find - they are probably too old for Army service in WW1 which kept records of parents etc on entry - school log books might help (some are kept at Museum) but not all have survived - otherwise the state was much less intrusive in peoples lives than today so official note of 'date of birth' much rarer.