Jonathan,
This appears to be your family in 1901:
http://www.census.nationalarchives.ie/pages/1901/Armagh/Glenaul/Annagh/…
And this is the birth of their son Walter which confirms Robert’s wife was Elizabeth Foster:
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1896/02186/1827035.pdf
Robert’s marriage in Keady 1st Presbyterian (which suggests Elizabeth was Presbyterian when she married):
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1883/10931/5993881.pdf
Robert’s probate file from the PRONI wills site. The will itself should be in PRONI.
Gillespie Robert of Annagh county Armagh farmer died 4 February 1929 Probate Belfast 30 July to John McWilliams and Thomas Marshall farmers. Effects £368 10s.
Also his brother Henry:
Letters of Administration (with the Will annexed) of the personal estate of Henry Gillespie late of Armagh County Armagh Farmer deceased who died 31 May 1877 at same place were granted at Armagh to Robert Gillespie of Annagh (Killylea) aforesaid Farmer a Brother and one of the Next-of-Kin and the sole Legatee.
Gillespie junior Robert of Annagh county Armagh farmer died 1 December 1926 at The County Infirmary Armagh Administration Belfast 8 June to Robert Gillespie farmer. Effects £5.
Gillespie Isabella of Annagh Killylea county Armagh widow died 4 June 1949 at saint Luke's Hospital Armagh Administration Belfast 17 September to Martha Roy widow. Effects £84 15s.
Regarding Robert born c 1846’s baptism, I note that though Tynan Church of Ireland has complete baptism records for that period, Killylea COI only has records from 1845. The church was evidently open before that as there are other records from 1829. So it’s possible he was baptised there in say 1844, and the records are lost.
Does this help?