I think this is the family you are looking for. If you agree, I have two more generations back and will send it. You can see Renze's name was spelled two ways.
Huwelijksakte Ferwerderadeel, 1841 Man:Rinse AEdes Pasma Vrouw:Fentje Pieters Landman Datum:26 augustus 1841Akte nr. 60
Their son Pieter:
Geboorteakte Het Bildt Aangiftedatum 16 november 1850, akte nr. 224 Pieter Postma, geboren 15 november 1850 zoon van Renze Aedes Postma en Fentje Pieters Landman
Renze and Fentje died in Het Bildt, Friesland. I know that their son Aede emigrated in 1883 with his wife and family. I don't know about Pieter but could look the next time I go to the library. Here is a possible marriage for Pieter, although Rinske's patronym isn't Klaas as you said, so it might not be the right couple:
Huwelijksakte Ferwerderadeel, 1875 Man:Pieter Postma Vrouw:Rinske Annes Koopmans Datum:15 mei 1875Akte nr. 27
Do you know what their wedding date was? Or were they married stateside?