Hi, Mollie:
I was wondering if you have had any luck since you posted, since it was back in 2012? Have you sent in your DNA? I am on Ancestry, MyHeritage, 23andMe, FTDNA, and GedMatch. I do have Joynt ancestors. But mine were from Shanaglish and just over into County Clare. It's about 24 miles from Shanaglish to Conicar and 27 miles from Tynagh.
I have DNA matches to the descendants of my great-great grandmother Anna "Annie" Joynt Fahey's siblings. She married Thomas Fahey of Keelderry/Doonally in Peterswell Parish. I have DNA matches to others with Joynt ancestors from Counties Galway and Clare. She was the daughter of Edmond "Ed" Joynt of Poulataggle, Kileedy, Clare and he died in Corofin, Clare, and Honor(a) "Nora" Larkin of Poulataggle, Kilkeedy, Clare and died in Beagh Parish, Galway. I have Larkin DNA matches to those from Counties Clare and going way back linked somehow to County Tipperary, many still living in Ireland.
Anna "Annie" Joynt Fahey and her brother David Patrick Joynt both lived in Shanaglish, Galway (near Gort) before coming to the USA. Their sister Mary Joynt Fahey lived in Gort/Beagh Parish. Their sister Honor "Norah" Joynt Carrig lived and died in Gort. Brother Michael "Ned" Joynt lived in Poulataggle, Clare. Their brother Martin Joynt was born in Gort and lived in Abbeyknockmoy, Galway (he married Mary Fahey). Probable sister Bridget "Biddy" Joynt was born in Tubber and lived in Abbeyknockmoy (she is listed as a witness in family baptism records). Probable sister Elizabeth Joynt Rabbit(t) was born in Tubber, Clare (Tubber is both in Clare and Galway) and died in USA. We think possibly maybe that Patrick "Pat" Joynt (Joyent) born in Tubber and died in USA (married Mary Connors) was their sibling.
The Joynt name is not super common in Ireland and those that were Catholic is a even smaller group. And those from County Galway and Clare seem to have a common connection.
Anna