There was still an Elliott family farming on Trasna Island in 1901 (it was the only house on the island:
http://www.census.nationalarchives.ie/pages/1901/Fermanagh/Ballycassidy/Trasna_Island/1363610/
Andrew married Ellen Graham from Trory in 1866. His father was William Elliott. Perhaps Peggy’s husband?
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1866/11534/8241891.pdf
Griffiths Valuation in 1862 lists Peggy as the tenant, so that indicates her husband was dead by that date. So no death certificate to be found but you might find a burial record in Trory Church of Ireland records in PRONI.
http://www.irishgenealogyhub.com/fermanagh/griffiths-valuation/parish-of-trory.php
No Elliotts on Trasna in the tithes for 1825.
The informant for Peggy’s death was Anne Jane Elliott of Trory Island who described herself as a relative. This looks to be her:
http://www.census.nationalarchives.ie/pages/1901/Fermanagh/Ballycassidy/Trory/1363587/
She was Anne Jane Hamilton and married William Elliott from Trasna Island in 1877. William’s father was another William, so presumably a brother to Andrew on Trasna in 1901:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1877/11124/8072850.pdf
1911 census for Trasna has 84 year old Andrew living alone on the island:
http://www.census.nationalarchives.ie/pages/1911/Fermanagh/Ballycassidy/Trasna/515279/
He died there in 1921, intestate. The executrix Margaret Davies might, at a guess, be a married daughter:
Administration of the Estate of Andrew Elliott late of Trasna Ballycassidy County Fermanagh Retired Farmer who died 30 October 1921 granted at Belfast to Margaret Davies Married Woman Effects £124 8s.
PRONI should hold the probate file which would supply more information.
On Trory in 1911, William & Anne Jane:
http://www.census.nationalarchives.ie/pages/1911/Fermanagh/Ballycassidy/Trory/515254/
Elliott William of Trory Enniskillen county Fermanagh farmer died 5 October 1929 Probate Belfast 2 May to James Seery farmer and Thomas Rankin land steward. Effects £102 15s. 6d.
Elliott Anne Jane of Trory Ballycassidy county Fermanagh widow died 12 May 1934 Probate Belfast 9 November to Selina Elliott spinster. Effects £34 5s.
There was another Elliott on Trory:
http://www.census.nationalarchives.ie/pages/1901/Fermanagh/Ballycassidy…
Administration of the Estate of Andrew Elliott late of Trory County Fermanagh Farmer who died 21 July 1904 granted at Armagh to Sara Elliott the Widow.
I’d expect he is related too:
http://www.census.nationalarchives.ie/pages/1901/Fermanagh/Ballycassidy…