There is a village and townland in Co. Armagh called Belleek, though not a parish of that name. (Belleek is in the parish of Loughgilly).. You can find Belleek easily enough on Google Earth. Type in Belleek, Newry, Armagh.
I cannot recognise Connanary as a townland in Co. Armagh. However you might need to make local enquiries on that.
The other Belleek, In Co Fermanagh is in the parish of Carn, so the information doesn’t really fit it perfectly either.