Elizabeth,
I found this death for a Hannah Ballentine in Feb 1901 aged 89. She was the widow of John Ballantine, a farmer. They lived in Gillistown which is about 4 miles north of Randalstown (and not too far from Ballymena). It’s in the parish of Ballyscullion Grange. So that all seems to fit with your information:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1901/05739/4620193.pdf
John had died the year before:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1900/05747/4622921.pdf
Probate of the Will of John Ballentine late of Gillistown Toomebridge County Antrim Farmer who died 10 November 1900 granted at Belfast to William H. Keilty and William Ballentine Farmers.
The above will is on-line on the PRONI wills site. Very short he just leaves everything to his son William.
This looks to be their son William in the 1901 census:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Ballyscullion/Gillistown/941372/
William’s marriage to Mary McMullen in 1878 (at Grange Presbyterian).
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1878/11086/8057360.pdf
John Ballantine is listed in Griffiths Valuation. He had plot 31 which was a 4 acre farm. Today that will be somewhere near the Largy Rd or the Gillistown Road.
I’d suspect they attended Grange Presbyterian church in Taylorstown but can’t say for certain. They may well be buried there but I don’t see any gravestones listed there for them so they may be in an unmarked grave. Presbyterians don’t generally keep burial records, so if there’s no gravestone, then it’s hard to know where they are buried. Photo of the church attached.
Here’s another probate abstract which names John:
The Will of Robert Ballintine late of Ardnaglass County Antrim Farmer who died 2 April 1880 at same place was proved at Belfast by John Ballintine of Gillistown and Robert Storey of Ballybollan both in said County Farmers the Executors.
Looks to me as though Robert of Ardnaglass (very close to Gillistown) was a relation. A brother perhaps?
The on-line Griffiths maps don’t show precisely where plot 31 in Gillistown was. There are copies of those maps that do. One set is held in Ballymena Library (local studies section). Upstairs. Ask for Enda. A good man. He’ll help you find the right map. Gillistown is very fiddly. It's spread across about 3 maps and the plot numbers are quite hard to make out due to fading & over-writing. Or an alternatove option might be to knock on a few doors on Largy Rd or Gillistown Rd to see if anyone knows the family. (Someone obviously did 30 years ago when your father went there). The family were still at the same location in 1930 according to the Valuation revision records on the PRONI website (copy attached).