James,
Here’s a David Lyons in West Quarter in the 1831 census. There were a total of 8 (5 males and 3 females) in the household at that time, all Presbyterian:
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Coleraine/…
There was a John Lyons living nearby who may be related:
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Coleraine/…
The townland of West Quarter is properly named Ballyleese (West Quarter of). There was a Daniel Lyons living there in Griffiths Valuation of 1859. He had plot 4 which was a 6 acre farm. (That farm today is up a dead end lane off the Kiltinny Rd). You can see where it is using the maps on the Griffiths site.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameS…
Daniel was deleted in 1874, and replaced by Daniel McIlreavy. No Lyons living there by the time of the 1901 census, but the McIlreavy family were there:
http://www.census.nationalarchives.ie/pages/1901/Londonderry/Portstewar…
A McIlreavy may have married a Lyons. You’ll need to investigate that.
Portstewart Presbyterian church has baptism records starting in 1829. The marriages start in 1845 (and are on-line on the irishgenealogy site). There’s a copy of the baptisms in PRONI in Belfast. Many churches are locked save when there is a service taking place, so if you would like to look around it, you need to contact the Minister in advance and make arrangements for someone to open it up. Your Lyons family appears to have left the area by the 1880s, so the likelihood of anyone knowing anything about them 150 years later is not high, but they should know if anyone named Lyons still attends the church. (The McIlreavy family were Congregationalists. I think the nearest Congregationalist church would be in Coleraine. PRONI has these records for that church: Baptisms, 1837-50 and 1859-81; marriages, 1847-8 and 1855; burials, 1844-9.)
Tradition was to marry in the bride’s church. In this case David & Rose may have been attending the same church. There are 3 Keith families in the Portstewart area in the 1831 census. All were Presbyterian. So if they married in Portstewart Presbyterian church, in the 1830s or earlier, there’s no record to be found.
Regarding school records, Portstewart National School’s attendance records are in PRONI under SCH/60. I do not know what years they cover.
Regarding death records, I see a death for a Rose Lyons on 9th July 1873 aged 68, registered in Coleraine. Have you looked at that? You can view the original certificate on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
Here’s what looks like David Lyons death in Agherton, 1889 aged 89, and a widower. Note that the informant, a McIlreavy, was his son in law.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…