Hi Marlene,
Looks like you're in luck as the parents' marriage record is on www.rootsireland.ie/ & is quite comprehensive:
Date of Marriage:24-Nov-1856
Parish / District:COLERAINE REGISTRAR'S OFFICE
County:Co. Derry
Husband David Swinney Address:Kirkistown, Ballyrashane Denomination:Registrar District Occupation:LABOURER Status:Bachelor (Previously unmarried)
Wife Martha Connor Islandmore Ballywillin Registrar District Spinster (Previously unmarried)
Husband's Father James Swinney Occupation:LABOURER
Wife's Father Name: Alexander Connor SHOEMAKER
Witness 1 Thomas Forsythe
Witness 2 Peggy AnnCrawford
Children's baptisms from roots:
Name:Anne SweenyDate of Birth:25-May-1861
Date of Baptism:15-Jul-1861Address:Culhamin [calheme (?) Ballymoney] Near PortrushParish/District:BallywillinGender:
CountyCo. Antrim
Denomination:Church Of Ireland
Father:David SweenyMother:Martha /Occupation:Labourer
Name:David SweenyDate of Birth:15-Mar-1864
Date of Baptism:29-May-1864Address:Crossreagh [co Londonderry]Parish/District:BallywillinGender:
CountyCo. Antrim
Denomination:Church Of Ireland
Father:David SweenyMother:Martha /Occupation:Labourer
Name:Margaret Jane SweenyDate of Birth:28-Sep-1866
Date of Baptism:24-Feb-1867Address:Ballylaggan [ballylagan]Parish/District:BallywillinGender:
CountyCo. Antrim
Denomination:Church Of Ireland
Father:David SweenyMother:Martha /Occupation:Labourer
Name:Martha SweenyDate of Birth:9-Apr-1869
Date of Baptism:30-May-1869Address:Ballylaggan [ballylagan]Parish/District:BallywillinGender:
CountyCo. Antrim
Denomination:Church Of Ireland
Father:David SweenyMother:Martha /Occupation:Labourer
I searched for David Sweeney with father James but the earliest was 1867!
There is only 1 Sweeney (& no Swinneys) in the 1851 Irish Census
If you haven't already you may want to try geni.nidirect.ie/
Col