Ballymena is in the parish of Kirkinriola.
Islandstown is a townland of 194 acres. It?s about 7 miles north east of Ballymena on the A43 Cushendall/Glenravel road leading to Cushendall. Islandstown Rd runs off this to the south, and at that point you are in Islandstown.
Tradition was to marry in the bride?s church. So that would be the place to look for Eliza?s baptism and family. From the information you have given it appears the marriage was in Skerry & Racavan, Church of Ireland. That?s St Patrick?s and is in the main street in Broughshane. Their parish records start in 1802, and there is a copy held in PRONI, Belfast (the public record office).
You can also contact the church but many churches here are inundated with genealogy enquiries and you may not get a prompt reply. If the rector/vicar agrees to look up the records for you, there is a fee of ?19 per hour. You may find it easier and cheaper to look up the PRONI copy when you are in Ireland. Ref: MIC1/78. If you do want to contact the church, here?s a link to it?s website:
http://www.stpatrickschurchbroughshaneanglican.org.uk/
Winning is not a very common name in the Broughshane/Skerry area and I cannot find a reference to Eliza?s family in Griffiths Valuation or for the marriage or death of her father Peter in the Irish civil registration records.
You have given David English?s address as ?Brochain?. I think this is a mis-spelling of Broughshane (which would roughly be pronounced Brochain. The ?ch? is soft as in Loch Lomond).
There was a Samuel English who, in 1863, had a house and outbuildings (plot 14j) on the farm of Alexander Davison in the townland of Knockboy (near Broughshane). Samuel looks to have been born c 1793 and died Jan ? Mar 1883. There was also a James English who lived in William St, Ballymena at that time too. I have no way of knowing whether these are relations.
There?s this gravestone in 1st Broughshane Presbyterian churchyard:
English First Broughshane Presbyterian Church 1780 Here lyeth the body of Janet Cahoon who died Nov 14 1780 aged 55 yeas wife to John English with 4 of his children
I can see a death in the statutory records that fits your information about Eliza English (nee Hammond). Tipperary town Apr ? Jun 1878 Volume 3, page 577. You can order a photocopy of that cert from GRO Roscommon for 4 euros. http://www.groireland.ie/