Hi, thank you so much for taking the time to respond! The Quinlans were all Roman Catholic. Every piece of information that the family has simply says they were all born in County Cavan. We do have some Graham relatives who were born in Armagh and moved to Monaghan -- also all Catholic. Nobody in the family history (Quinlans and the people they married) has ever shown up as Protestant, and all were strict Irish Catholics. The family history basically starts with U.S. immigration, so that's why it's been so difficult to find Irish locations and cemeteries for Quinlans in particular.
I found a baptismal record for my great-grandfather Thomas Quinlin (who immigrated to the U.S.) on roots-ireland. Lists the date as 10 Oct. 1844, matching family records. Father: Thomas Quinlin, mother: Nelly Connelly. Address: Killiliss, parish Knockbride. Sponsors Nelly Carlin and Patt Cooney. And then there's an odd note: "see also THOMAS KINDLAN AND ELLEN CONLEY." So I'm also searching for Kindlans, though nobody in the family has ever noted that spelling. Quinlan itself has many spellings, which could be partly why I've reached a dead end.
The death record is 1877 for my 2nd-great grandfather Thomas Quinlan (did not immigrate to U.S.), has address Killiliss, Co. Cavan, parish Cootehill. Death age 84 corresponds to family history. Says he was a married farmer and lists Alice Quinlas as informant (daughter Alice again matches family history) and that he died of a heart ailment.
So we know Thomas and Ellen lived in Cavan during their marriage and at their deaths, and their children were born there, most of them immigrating in the 1860s to the U.S. But I imagine you're right that they may not have been from Cavan originally, which of course will probably remain a mystery.
I've found Graham relatives' gravesites in Monaghan and will visit there, but planned to head to Cavan, as well, hoping to find some Quinlan roots -- that is the family name that comes up most often in our extended family, which is very large now.