Bill, I came across your Nivison family while searching for mine! The information I have is from 1880, 1870, 1860 census images.
Condensed version: 1860 Michigan Branch Batavia William Nivison - 46 - New Jersey Catherine - 38 - New York William E. - 19 - New York (there are other siblings and an uncle?) 1870 Michigan Branch Batavia William Nivison - 54 - New Jersey Catherine - 47 - New York William Nivison - 26 - New York Belle 24 - Michigan Minnie - 2 - Michigan William D - 1 - Michigan
1880 Michigan Branch Batavia William Nivison - 64 - New Jersey Catherine - 60 - New York
1880 Michigan Branch Girard William E Nivison - 37 - New York Bell - 33- Michigan Minnie A - 13 - Michigan Willie D - 11 - Michigan Archie E - 1 - Michigan
I found my "William Nivison" in Branch County, Algansee Twp in the 1870 census.