The 1859 marriage certificate gives John Scott’s townland (address) as Drumshannon. That’s in the parish of Aghabog, near Clones, and is in Co Monaghan. Griffiths Valuation for 1861 lists George Scott in that townland (along with some other Scotts). George’s farm was plot 13 which was a combined total of about 12 acres. It would be easy enough to locate that today if you wish. (It’s still farmland but the farm and outbuildings have gone).
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNameSearch&familyname=&firstname=&offset=20&countyname=&parishname=&unionname=&baronyname=&totalrows=26&PlaceID=1036123&wildcard=Tradition was to marry in the bride’s church. They married in Clones Presbyterian so that suggests at least she was brought up that denomination. Unfortunately Clones Presbyterian only has baptism records from 1856 onwards. I am not sure if that’s because it only opened then or whether earlier records have been lost. The only Presbyterian church in the Clones area with records for the 1830s when Ann was born is Stonebridge. They start in 1819. I don’t think they are on-line anywhere but there is a copy in PRONI (the public record office) in Belfast.
If John Scott was also Presbyterian then there is a Presbyterian church in Drumshannon. I think it may be called Drumkeen. Possibly his family church. If so, again it only has baptism records from 1856 though marriages go back to 1845.
There’s a possible death for George Scott registered in Clones in 1869 aged 65. You would need to order the certificate to check it’s the correct man. George Scott is listed in the 1833 tithe applotment records for Drumshannon. Farmers didn’t move around much so that’s likely where John Scott was born.
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp There was 1 Scott family still farming in Drumshannon in 1901:
http://www.census.nationalarchives.ie/pages/1901/Monaghan/Killeevan/Drumshannon/1632021/Probate of the Will of William Scott late of Drumshannon County Monaghan Farmer who died 25 September 1908 granted at Armagh to Marshall McCaldin Wright Millowner J.P. and Edward McCaldin Merchant.