Oakpark (officially Oakpark Demesne) townland was in a detached portion of Painestown civil parish, based on the census this family were 'Irish Church' so Church of Ireland, the parish church was at Dunganstown a short distance to the west of Oakpark.
Unfortunately a check of the latest RCB parish list shows that early Painestown Church of Ireland records going back to 1698 have been lost and all that is available is records from about 1830 in the RCB Library with a copy at the National Archives.. Some records for the parish from about 1833 are included on IrishGenealogy, some of these appear to be from a Chapel of Ease.
The area is very close to townlands in Carlow (town) Church of Ireland parish, so worth checking these -they are apparently included on the free IrishGenealogy website back to the late 1600s.
To try tracing forward you could try the 1911 census and civil BMD records up to the cut-offs. I had a quick look on the 1911 returns but the family seem to have all left - only Jacob at Oakpark by that time is a 50 year single man named George Jacob ..no sign of any Pierce surnames either (Elizabeth's Anne maiden surname) in OakPark/Painstown that I could see on either the 1901 or 1911 returns, based on the marriage she lived for a time in Co. Kilkenny - Paulstown/Grangesilvia
p.s. this George may be the same George Jacob a witness to John and Elizabeth Ann's marriage