I found three references to the name BINANE in Kerry - baptism and sponsors.
They might not be relevant, but prove the existence of the name BINANE in Kerry.
I think that the name BEHANE should be used in the search.
Behane/Behan/Bennett are also corruptions of the name BUNYAN or Bunáin.
There is a baptism in Tralee (6th March 1859) of Patrick Behane, with a father named Michael Behane.
This might not be relevant, but is a start.
Regards
antocar1913