I had a look in the Rev Parks’ 1817 census of Ballymoney parish. There were 5 Kennedy households but none with a Hugh, Helen & John listed. There was one John but his parents were Neal & Rachel. There was also a widow Kennedy but she lived alone.
There was no-one named Templeton in Ballymoney at that time.
Likewise there was only 1 Murphy family , William, Sarah, Martha & John. No Helen (Ellen).
Regarding the name Helen, it is found in Ireland but mostly we use Ellen. However when people move to Scotland (as hundreds of thousands did), Ellen usually becomes Helen there, presumably being the more popular version. But when searching Irish records in the 1800s, it’s more likely to be Ellen rather than Helen.
The absence of either your Kennedy, any Templeton or a suitable Murphy family suggest your family came from somewhere outside the immediate parish of Ballymoney.
John & Margaret evidently married around 1825. That’s long before the start of statutory marriage registration (1864 for Catholic marriages and 1845 for non Catholic). You haven’t said what denomination your family was. Ballymoney 1st Presbyterian has baptism records starting in 1817, 2nd from 1835, the Church of Ireland from 1807, Methodist 1831 and RC 1853. There is also a Reformed Presbyterian church whith records as follows:
[There would appear to have been two meeting houses in the early 19th century – at Kilraughts and Dervock; Ballymoney meeting house was built in 1829]
Register of members by society with baptisms, marriages, deaths and removals including emigration, c.1835-44 (for Dervock and Ballymoney, but also records details for Ballymoney Society from 1804); register containing session reports,1914-81, that record deaths and births/baptisms, 1914-75, and admissions, 1914-75, with lists of members (the earliest ones recording details of deaths and emigration), 1914-88; call and attestation of call to the Rev. John Lynd signed by office bearers and members, 1886; committee minutes, 1890-1956; session minutes, 1845- 66 and 1886-1931, with list of elders, 1891 and 1893 which include details of their death; stipend account book with names, 1858-1906 with a list of members for 1868 and 1877.
The RC records are on-line though obviously they don’t go back to the period you need. The remainder are not on-line but there are copies in PRONI (the public record office) in Belfast. Personal visit required to view them.
Finding where John & Margaret originate may be tricky. Tradition was to marry in the bride’s church so that may not be the same church where children were later baptised. Not all churches have records for the 1820s and even when they do they are not necessarily on-line.
I looked at the surname Templeton in the 1901 irish census. There wre over 400 in Co. Antrim. The vast majority were Presbyterian, thogh there was a sprinkling of other denominations as you might expect. The only Templeton in the Ballymoney area was this lady who was a Reformed Presbyterian:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Ballymoney__Urban__and_Ballymoney_Urban_District/Union_Street/1009255/
Reformed Presbyterians are a separate denomination from Presbyterian and favour a stricter interpretation of the bible. Often known as Covenanters.
There was an agricultural census in Antrim in 1803. It lists a Hugh Kennedy in the townland of Livery, parish of Derrykeighan and another in Carrivcashel, parish of Loughguile. About 20 Murphy households but without Helen/Ellen’s parents names no way of saying whether any might be hers. There was a Templeton family in Ballyhibistock, parish of Derrykeighan, another in Dervock, parish of Derrykeighan and 1 in Cubbindall, parish of Ballymeoney. Also a widow Templeton in Drumard, parish of Ballymoney. Derrykeighan & Loughguile are very close to Ballymoney so all are possibles for your families. This link explains what records exist, parish by parish:
https://www.nidirect.gov.uk/publications/proni-guide-church-records
If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
