I don’t have the 1870 Branch County census to look at now, but I have most of the information you asked for. I also added information on Drusilla Nivison Goodman since she was also a daughter of Nathan and Matilda.
Nathan Nivison 60 NY Farmer Matilda 57 NY Keeper at home John 17 NY Farm labor
George Nivison 26 NY Farmer Katie 18 Ireland Keeper at home Ana 1/2 MI
Robert Nivison 34 NY Farmer Louisa 37 NY Keeper at home May 13 MI At school William 11 IN At school Edward 2 MI Clarie Goodman 14 MI At school
William Nivison 27 NY Farmer Mary 18 MI Keeper at home **Vernon 5/12 MI
George Goodman 40 NY Farmer Drusilla (Nivison) 32 NY Keeper at home Charles 13 MI At school Alice 10 MI At school
Batavia William Nivison 26 NY Farmer Belle 26 MI Keeper at home Minnie A 2 MI William O 1 MI
** Vernon was my great grandfather. He was moved to Seattle in 1904 and raised his family there. He died in 1958. I have more information on the Nivisons from Algansee-Coldwater if you are interested.