Sorry for the late reply, but I think I found the person you are looking for.
It is probably Bjinse Kornelis Rienks, born March 29, 1827 in Hallum, Friesland.
There is not very much info on this person in the book, but it looks like this info coincides with yours.
Apparently his father moved, in between 1833 and 1860, from Hallum to Froubuorren (Vrouwenparochie, Het Bild, Friesland).
So then Bjinse was about 26 years old when he emigrated to the States, but this can not be found in the book. Do you have more about this census in 1870? And are you in any way related to Bjinse?
I think you are interested in his forfathers too, so I'll give you the details, as far as I know:
Father: Kornelis Jehannes Rienks, born December 12, 1790 in Marrum. November 6, 1816, he married Baukje Hindriks Stelwagen from Hallum.
(This was a younger brother of my ancestor, Jan Jehannes Rienks, so from here on up our family lines go together)
Grandfather: Jehannes Rienks Rienks, born January 25, 1740 in Holwerd, died May 25, 1821 in Hallum. August 18, 1768, married Aukje Siedses Boersma, born August 17, 1750 in Marrum, died June 25, 1826 in Hallum.
G-G-father: Rienk Jehannes, born April 1, 1708 in Ferwerd, died 1768 in Wester-Nijtsjerk. In 1732 he married Klaske Klazes from Hallum, who died in 1779 in Wester-Nijtsjerk.
GGG-father: Jehannes Rienks, born 1672, died 1756 in Ferwerd. In 1707 he married Sytske Symens.
GGGG-father: Rienk Oenses, born July 27, 1626 in Hallum. May 21, 1671, he married Hiltsje Tjittes from Blija.
And finally: Oense Rienks, born 1590, died 1633 in Hallum. In 1618 he married Sijke Peters, born 1602 in Ikkerwâld.
If you want to know more about the Rienks family and want to gain access to our Rienks Family Website, please mail me.
This website can only be viewed by people who are invited by members, but besides that there are no further obligations.
I surely would like to hear from you again!
Ad Rienks, Sliedrecht, Netherlands