First of all we can derive little meaning from the current spelling of the name. Feige has two meanings: as a noun it's a fig, and as an adjective it means cowardice. Feighner is indeed a German name derived probably from Feichtner. Feichtner is a name that is common in today's Munich or Berlin in Germany. When the Feighners immigrated to America in the mid 1700s I could only guess that the name was misspelled in the records, as "gh" has no occurrences in German. An alternate spelling is Feuchtner where "feuchte" means damp or moist which I would not tie into anyone's name. What "Feichtner" means I haven't a clue.
The German word for bird is "Vogel" and not FEIG. My main hobby is birding. Therefore the first part of my email address is "feinerVogel" meaning "fine bird" which comes close to our name.
Mike Feighner, Livermore, CA