I can't see any entries around that time with William Owen Jones as the father.
There are a number of births with Jane Costain as the mother with no father given. e.g. Margaret Jane COSTAIN [born] 17 Nov 1884 [place] Ramsey, [father]Not given, [mother] Jane COSTAIN. [From Brian Lawson's Births file.]
However Civil registration of births in the IOM was not compulsory until 1878. If it took place in the IOM you should be able to find his bapt on the IGI?

Their marriage is in the Maughold register, so the above Jane is unlikely to have been her:
22 Jan 1867
Owen JONES Full age Bachelor, Quarryman, [residence] Ramsey, [father] John Owen, Quarryman, and
Jane COSTAIN Full age Spinster, [residence] Ramsey, [father] William Costain, Joiner.

Note that his name was given as Owen, not William Owen.

- Have checked IGI, which has:
name: John William Jones
event: Christening
event date: 10 Nov 1871
event place: Maughold, Isle of Man
gender: Male
father: Owen Jones
mother: Jane Jones
digital folder number: 004498206

It isn't on the Maughold register transcripts I have, so I'm wondering whether it was in Ramsey (town which is partly in Maughold parish).

Also on IGI:
name: William Jones
event: Christening
event date: 15 Nov 1867
event place: Maughold, Isle of Man
gender: Male
father: Owen Jones
mother: Jane Jones
digital folder number: 004498206

The Maughold parish register has:
William JONES aged 4 mths, of College St, Ramsey, buried Maughold Mar 24 1868.

Sue