The Rev. John Denniston's teacher (according to Alumni Dublinenses) was a "Mr Balantine".
According to William Roulston (in Restoration Strabane, 1660 - 1714, p55):
In 1714 the 6th Earl of Abercorn (Captain James Hamilton) turned his attention to the educational needs of the town when he founded a school in Strabane and endowed it £32 per annum out of lands in Ballysinode, part of his estate in Co. Tipperary. The rectors of Taughboyne, Donagheady and Camus and the provost of Strabane were to be its perpetual trustees.54 It was probably at this school that Mr. Ballentine taught; several of his pupils went on to study at Trinity College, Dublin.55
Note different spelling of Balantine/Ballentine here and in Alumni Dublinenses.
Footnotes:
54 PRONI, MIC/1/35, Donagheady vestry minute book; RDD, 86.475.61388
55 Burtchaelle and Sadlier (eds), Alumni Dublinenses, pp 363, 527, 545, 753 (John Denniston appears on p224 of the 1835 editon - SD)