There does not appear to be a common ancestor in recorded history. I have a quite a bit of information from Wolfau village records that may have come from the Burgenland Bunch Newsletter. If you have not visited its site, you may want to do that as it is a wonderful resource. Here is some information you may find interesting.
Ab and Lavern Karner (OK relatives) twice visited Wolfau, Austria and the area where Michael Karner our immigrant Karner, came from. They visited excavations at Petronell and Deutsch Altenburg begun in 1852. Pettronell covers the Palace Ruins Roman complex constructed in the 4th Century AD and is located 32 miles east and a little south of Vienna. One of its buildings is called “Rundbau” (round building) and contains the KARNER. According to history the Karner was a building (or room) used as a repository for human bones.
Franklin Karner (another Michael Karner Oklahoma relative) stated “Everything I have read and researched indicated several possibilities for name origin. I have read the name Karner is from Kartner, a province in Southern Austria. Some think it means “builder of carts”.
Margaret Flasch (my mother in law and granddaughter of Michael Karner) had a photograph of who she remembered as being identified as Michael Karner’s brother, Johann and his two children (see photo below). Margaret said Johann was the oldest Karner child and that he was a bookbinder by trade.
Helen Holmes (another granddaughter of Michael Karner's) remembered that her mother (Theresia Freudenberger nee Karner) told her that Michael Karner’s father, Johann, had been a bookbinder in Frankfurt, but had been chased out of that town during the revolution of 1848. Helen added, “Bookbinders, while perhaps not on the cutting edge of the intelligentsia, were of course in contact constantly with men of letters. In those days, remember, binding of books was not a common thing; usually done for those seriously interested in collecting a library. Leather bindings and all that. Craftsmanship, etc involved. Plus exposure to ideas. Anyway, once chased out, he went back to the home village, (presumablely Wolfau) merging with the bone handler – farmer clan. At least, that is how I recall Mother’s story.”