Hello Glenda, a mystery indeed, anyway I found only one Sarah Jane Weeks born in 1833 plus or minus 5 years, she was born in Limerick to father Archibold Weeks of the 6th Dragoons and was baptised in the Church of Ireland (Anglican or Protestant) in St Johns Parish on the 3rd February, could find no siblings. This does not meet your brief though.
I could not locate the marraige and found one child baptised in Dublin at the Pro Cathedral, near the main street O'Connell Street in 1865, address was 6 Carisle Cottages. in the church record the name is spelled Neille, this is a free site and all civil records commenced in 1864, sign in under Church for the baptism, I notice the civil records gives No 9 Carisile Cottages, attached below, under the church records I searched under Weeks as it brings back the mothers name too for ease of finding and the spelling was Neille, on the civil record the addres appears to be in the south of the city on searching for it. I did not search for any more and got no more under weeks in the baptisms. https://www.irishgenealogy.ie/en/ The site is free and enter under Church or Civil and follow instructions and sign in, you can sign in as anybody it is a trust thing.
There is a Thomas Neil mother Mary Farmer born in 1831 in Mealagh, Parish is Windgap, Kilkenny, father is James, baptism is 24th July, there are also siblings to this marriage, Patrick 1823; Catherine 1825; Ellen 1827; Michael 1833; Mary 1829; this is the only Neill with a mother Mary Farmer, Kilkenny is adjacent to Wexford not beside it but close enough, also near Waterford, you can see the church records here, can only search by month and year and then read, https://registers.nli.ie/parishes/1034 records only commence in 1822 August I think.
Remember that the records may not exist and that I only found was is online, other areas have records starting later so it is guess work and you need to find more information to be definite, remembering it will not be easy,
In Griffiths Valuation in 1853 circa there is only one Farmer family in Kilkenny and a few in Wexford, oddly the entries for Wexford are mainly for a Rev Hugh Farmer who is a landlord, there is also a Rev Henry Farmer also a landlord, in case it means anything to you. This is a major land survery that recorded owners and tenants only. http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSe...