The 1919 death certificate for Sarah Jane shows she was living at Gortacloghan, Co Derry and her daughter Charlotte Wade of the same townland was the informant:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1919/05165/4424606.pdf
So these 2 Wades in Gortacloghan in 1911 may well be related to Sarah Jane:
http://www.census.nationalarchives.ie/pages/1911/Londonderry/Slaght/Gortacloghan/591374/
1853 marriage cert gives you William & Sarah Jane’s fathers names:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1853/09447/5422534.pdf
Tradition was to marry in the bride’s church so Desertoghill Church of Ireland is perhaps where she was baptised. Unfortunately their early records were destroyed in the 1922 fire, so you may not get very far with that. Both were living in Lisachrin when they married.
Couple in 1901:
http://www.census.nationalarchives.ie/pages/1901/Londonderry/Grove/Carbalintober/1521529/
I can’t see the couple in the 1911 census, nor can I see a death for William in 1912 in the Coleraine registration area.
Here’s a marriage for Charlotte Irwin and James Wade of Gortacloghan in 1897. Her father is given as Joseph Irwin though not William Joseph.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1897/10441/5801930.pdf
Here’s the family in 1911:
http://www.census.nationalarchives.ie/pages/1911/Londonderry/The_Grove/Carbalintober/592564/
If you are looking for William Joseph & Sarah’s births, they were born before birth certificates began in Ireland (1864) and so you would need to search for their baptism records. They may not exist or if they do exist they may not be on-line. You may need to go to PRONI in Belfast for them. You would need to know their precise denomination and where they were baptised. How sure are you that they were both born in Portrush? That is some distance from the general locations the family were living in other records. (They were all around Garvagh which is about 20 miles away).
Here’s the birth of a son William in 1875, in Coolbane (Cuilbane).
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1875/03094/2134407.pdf
There also looks to have been a daughter Anne on 11.12.1866.