I'm fairly confident that your family is the same as the family whose biographical sketch I submitted. I do not know anything more than what I entered. I have done no research on them.

The two different spellings (Cuningheim vs Koenigheim) are not surprising. I found a third spelling on Google Maps, Konigheim apparently in the state of Baden-Württemberg on Road 27 about 5 km west of Tauberbischofsheim and 100km north of Stuttgart.