I too am interested in Christian Dietz/Elizabeth Carmer.
There is an undocumented description at familysearch.org that names David Dietz as the son of Christian Dietz and Elizabeth Carmer.David is listed as born in ca. 1796 in Eddyville NY. I can't create a link, but searching their resources for 'david dietz' will pull it up; if not, let me know.
I have other evidence that my ggggrandfather was David Deits, born ca. 1796 in the same town.He married Patience Tilson and moved to Wisconsin.This is documented in the Tilson family history.He used the Deits spelling (many documents) which our family continues to employ.
I would be happy to know if you come up with additional information about Christian Dietz and would by glad to share what I have.