My research mainly involves the various places that prisoners were place on board the "Lively" tender/barque with Captain Christopher DOBSON as I am tracking the movements of my ancestor who was tried in Athy in 1797. I am unable to find out as yet his prison place between Athy and Dublin??
The Lively went from Dublin to Cork and the convicts were place on board the "Minerva".
My first guesses if he was held in County Kildare would be either Athy or Naas.
Athy gaol was in White's Castle 1730-1830s.
Confusingly the prison in Naas was known as White's Castle Gaol. It was in use from 1786. The site was later occupied by the Town Hall which has recently become a library and cultural centre. Historical information on Libraries section of County Kildare website
https://www.kildare.ieThere were convict depots for prisoners awaiting transportation. Kilmainham was a convict depot. It was built to replace an older prison in 1796.
Information about Irish prisons and resources on Irish Genealogy Toolkit.
https://www.irish-genealogy-toolkit.com/irish-genealogy-search.htmlA-Z contents list: Courts; Crimes; Prison Records
"History Ireland" journal has some articles about prisons e.g. "A scene of shameful disorder and dissipation" names several prisons
https://www.historyireland.com/a-scene-of-shameful-disorder-and-dissipation/Putting search term prison or gaol or convict or transportation may find more articles.
Have you looked for newspaper reports of the trial? They may mention where the convicted prisoners were taken.