Can't help you with Michael, but I do have an Elizabeth who was born 18 Oct 1782 and died 29 Aug 1871, according to my database. I have her and 5 other siblings tentatively assigned to parents, but cannot verify the link at present.
_IF_ she's the right one, then she belongs to the family of William Abernethy & Sarah Samuels, from Northern Ireland. Probably the daughter of son James & Anne Clarke rather than any of William's other sons, since John and Samuel's daughters by that given name are said to be Mrs Richard Wilson and Mrs Patterson, and I have no evidence that son William & his wife ever had a daughter named Elizabeth.
You can find William's will in the documents section ofhttp://bellsouthpwp.net/n/s/nss8660/dna/dna.htmlhttp://bellsouthpwp.net/n/s/nss8660/dna/dna.html. Pedigrees of some of William's descendants can be found from theY-DNA data results pages, along with other probably related Abernethy families that have been traced back to Northern Ireland.