That depends on which James Canty you're seeking! I assume that the Teige Canty you mentioned is the one who got a 420-acre land-grant, adjacent to George Canty, on 23 Aug 1672.
The James Cantey who was born in 1755 in Camden District (d. 9 oct 1817 in Milledgeville GA) is presumably the son of John Cantey (d. 1792) and Mary McGirt (b. 1733), presumably the husband of Martha Whitaker (b. 1746 in Halifax NC, d. 9 May 1801 in GA), daughter of James Whitaker and Catherine Wiggins. I have no idea if any of that info is accurate, since I haven't seen the documentation myself.
I can ID the wife of the earlier James, since I've seen those references. Book D, p. 269, 8 Apr 1725. Deed of Sale. James Cantey, planter, & Elizabeth his wife, of Ashley Ferry to John Hill, carpenter, of Dorchester, for £300 current SC money, 100 a. on Ashley River between Peter Goulding's land and land formerly belonging to Charles Tredwell, which was bought of David Batcheller & devised to Elizabeth Cantey by will of her father John Stephens of Berkeley Co. Witnesses: William Wallace, George Cantey, Margaret (her mark) Arden. Receipt dated 1 Mar 1724 of £ currency & John Hill's bond for £200 payable 20 Mar 1725. Before Thomas Waring. Jacob Motte, Register.
The wife of this James was definitely Elizabeth Stephens, but it's not certain that these are the grandparents of that younger James. There were Canteys/Cantys all over the place in backcountry SC, and the family was a very prominent one, especially during the Cherokee Wars. Capt. John Canty, Capt. Samuel Canty, and Capt. James McGirt each led a company under Col. Richard Richardson in 1759-60. (Your James who married Martha Whitaker was far too young to be mentioned on the muster-rolls at that time.)