Hi Lesley,
There are many immigrants for USA whose birth place appears , in passenger lists, as Kunar, Kunary, Kunarz, Kunara or Kunari. There are also variations of the above mentioned names; Konar, Konary etc. Most of these immigrants were of Polish origin (some from Galicia, others from Russia). Probably the place you are looking for, is a very small shtetl and that is the reason why you can't find it using J G townfinder. From what it appears, there are a number of small villages in Poland named Konary. Perhaps if you knew the gubernia or the district that Kunar belonged to, you could locate it more easily.
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Giannis Daropoulos
Greece