This is a shot in the dark.
Check out http://www.lecalehistory.co.uk/1901/townlandlist.htmhttp://www.lecalehistory.co.uk/1901/townlandlist.htm and specifically "Ballykinler Upper"
in house no 12, Thomas McGivern, an elderly farmer, is listed as living with his sister and "James Roney" a "servant".
The property involved is a small holding ( I actually know it) and its humble. The term "servant" is misleading or lacks context. I know from my other researches that James was a "cousin" or "relative" and in fact he inherited the farm on Thomas death.
I'm wondering if Thomas and your Mary Anne are related.
Saul is just about 10 miles from Ballykinler. While Rooney/Roney and variants is a reasonably common surname in the area, McGivern was relatively rare in East Down at that time.
This James would have been born in 1873-ish. So the dates wouldn't rule out a relationship.
Do you have any more info on the names of Mary Anne's children. Or perhaps you have a copy of the marriage certificate?
Its probably unrelated but I figured it was worth exploring!