Achonry (/æˈkɔːnriː/; Irish: Achadh Conaire, meaning 'Conaire's field') is a village in County Sligo, Ireland.The old name is Achad Cain Conairi. St. Nath Í ua hEadhra (O'Hara) founded a monastery here. The foundation gave the later diocese its name. The monastery was founded on land granted by the Clan Conaire. Nath Í was the teacher of of Ballysadare. The diocese was co-extensive with the barony of Leyney (Luighne).