It's very much a long shot, but I may be able to help a bit. I have my family in Ireland traced back for over 200 years, but have one great-grandmother whose birthplace I still haven't located, and there is a chance that the maiden name of her mother, who would have been a bit younger than than your Conly, was Mary Nowlan. I've located a possibility for Mary in the parish of Gowran in Kilkenny. If you want to try checking your kit againast mine in GEDMATCH, my kit number there is T780556.
The Irish name Ó Nualláin (derived from the word nuall, menaing "shout") was anglicized in several ways, including Nolan, Knowlan, Nowlan, and Nowland. The main Ó Nualláin sept (tribe) originated in Carlow, which is just to the east of Kilkenny. Some of them migrated to Connacht, and are now found in Mayo and Roscommon, and there are unrelated Nolan families in Kerry and in Ulster. However, from my (amateur) research, the Nowlan(d) anglicization appears to be most common in Carlow and Kilkenny, especially in Gowran and nearby parishes, and across the border in Carlow (where the name is even more numerous). I have many fairly close dna matches in both areas.
The baptismal and marriage records in Gowran only go back to 1809 and 1810, respectively, but the records in some nearby parishes go a good bit further back. For example, Thomastown, which is just west of Gowran, has records back to 1782, so Conly might be found there. I've already searched all of the parish records available online for Kilkenny and Carlow, but for a later period than what you want. if you do find a genetic connection to the area, then you could search the earlier parish records in parishes which have them (which might be worth searching anyway, whethe ror not you find a genetic connection to me or anyone else) and it may also be possible to find Conly in old estate records (records kept by the landlord's agent which can contain a lot of helpful info), if you can find out where they are archived (local genealogical societies can often help with that).
If you want to try the Thomastown records, here's a link to use, and you'll see an interactive map there allowing you to move to other nearby parishes: https://registers.nli.ie/parishes/1032
