Cooneen is in the parish of Aghalurcher. The 1821 census for that parish has mostly survived but unfortunately the townland of Cooneen is not listed and there are no Trimble or Scott households in the parish.
The 1833 tithes for Cooneen list a Robert and George Scott as both being in that townland. Both would have had land to be listed in the tithes so were presumably farmers. So that provides some confirmation of the Scott family living in Cooneen.
http://www.irishgenealogyhub.com/fermanagh/tithe-applotment-books/parish-of-aghalurcher.php#.Wu1NJRR9eg0
Griffiths Valuation for 1862 does not list any Scott households in Cooneen indicating both families had left by that time.
Next step is probably to search church records for your ancestor. You haven’t said what denomination she was, but judging by the 1901 census for the county the majority of Trimbles were Church of Ireland plus a few Presbyterian.
There are 6 Church of Ireland churches in the parish (Aghalurcher, Cooneen, Lisnaskea, Kiltermon, Fivemiletown & Maguiresbridge). However some only opened in the 1800s. The only ones with records for the period you are interested in are Aghalurcher whose records start in 1788 (Baptisms) and 1801 for burials and marriages. Lisnaskea start in 1804 (baptisms, marriages and burials). Copies of both sets are held in PRONI (the public record office) in Belfast. A personal visit is required to view them. (The records don’t appear to be on-line anywhere).
Nearest Presbyterian church is Cavanaleck but they have no records earlier than 1853.