Griffiths Valuation for 1863 lists Alexander Stewart in Shannaghan, on plot 30, which was a farmhouse, outbuildings and 5 acres of land. His name remains against that property in the revaluation records until 1885, when he was replaced by a Robert Stewart (a son perhaps?). Robert in turn leaves in 1891 and is replaced by Mary (?Alexander?s widow), whose name remains against the property till 1928 when the occupant was an Alice Mc (illegible).
This looks to be Mary in 1901 (with a McElroy grandchild):
http://www.census.nationalarchives.ie/pages/1901/Down/Balloolymore/Shannaghan/1201687/
And in 1911:
http://www.census.nationalarchives.ie/pages/1911/Down/Balloolymore/Shanaghan/205551/
Does the 1849 marriage certificate give Shannaghan as Alexander?s townland at that time (and occupation farmer)? If so, that may be about as close as you are going to get to proving it?s the same man. (He?s the only Alexander Stewart/Stuart in Grifffiths at that time).
I note that the family were Presbyterian and their house was next Katesbridge Presbyterian church so I suspect that?s probably where they worshipped. If so, their baptism records only start in 1866, so that will probably be too late to find Jane and her siblings.
I looked for Alexander?s death c 1885. Closest I could find was registered in Banbridge in Jan ? Sept 1880, est year of birth 1786 (making him 63, if it was he who married in 1849. Was it a 2nd marriage perhaps? Was he shown as a widower on the marriage cert?).
You could search the tithe applotment records for Shannaghan (c 1820/1830s) to see if Alexander or his father are listed then. (Those for Co Down are not on-line. There?s a copy in PRONI, Belfast).