Ballywonard?
Have you looked for other names there in 1826 to see if you can locate where they lived?
http://www.irishgenealogyhub.com/antrim/tithe-applotments/belfast-parish.phpBigger, Mathew Townland: Ballywinnett Year: 1826
Bigger, Samuel Townland: Ballywinnett Year: 1826
Bigger, William Townland: Ballywinnett Year: 1826
Burney, John Townland: Ballywinnett Year: 1826
Burney, Widow Townland: Ballywinnett Year: 1826
Gaffen, Hugh Townland: Ballywinnett Year: 1826
Gilmore, Wm. Townland: Ballywinnett Year: 1826
McIlheggan, Nathl. Townland: Ballywinnett Year: 1826
McMullen, Jas. Townland: Ballywinnett Year: 1826
Russell, John Townland: Ballywinnett Year: 1826
Smith, John Townland: Ballywinnett Year: 1826
Also mentioned here-
https://archive.org/stream/historyoftownofb00benn/historyoftownofb00benn_djvu.txtThat the Churche in the Towne of Belfast bee continued a Parrish Churche where it is, and that the Three Townes of Ballycloughly, Ballyfinnoghy, and Dunmurry now of the Parrish of Drumbeg be added to the said Parrish of Belfast to all intents and purposes, and that in lew thereof the Townes of Bally coustan, Ballybought, and the halfe towne of Ballywinnett now of Belfast Parrish be hereafter separated from it in regard they lye above three myles distant from the churche of Belfast."
Just before posting this reply I found the following snippet which confirms my initial guees-
Belfast Commercial Chronicle, 18 Nov.1839: ... which said springs, streams, rivulets, and rivers, are situate the
Townland of Ballywonard, otherwise Ballywinnett, Ballyvaston, and Ballybought, in the Parish of _, otherwise Shankhill, and Carnmoney, Giengormly, ...