Laura, The Abstract for the will of Elizabeth Livingston is found in "Abs. Wills Chas. Dist. 1783-1800": ELIZABETH LIVINGSTON. Son: Joseph Henry, under age & unmarried, residue of estate. Sister: Isabelle Roberts. Niece: Ann Roberts. Exors: sister; James O'Hear of Charleston; Andrew Cunningham of Horshoe. Wit: John Bryden, John Norris. D: 17 Nov 1783. P: 4 Aug. 1784 from p. 376 of Will Book A 1783-1786
There is a booklet called "Livingston & Carlton who are we?" Henry Newell Carleton, New York, Feb 1966 p. 73 begins a chapter on "The Fabians of Toogoodoo" and the chapter ends on p. 82 saying that Elizabeth Fabian (c1753-1784) married John Livingston in 1772. The following two chapters are about John Livingston & their son Joseph Henry Livingston (c1773/80 - d. Oct. 1811)
Joseph Henry's will is on p. 89. There is also much about the Stent family [which is my connection].