I have been chasing this mystery for a few years and I have decided to post the question on to the Kinnison/Kennison forums.
From various dated Obits. and death certificates in this family:
According to the Beaver Funeral Home and her death certificate (her name is spelled Armanda Cottreal on both records), the name of her mother was unknown and her father was Vanscoy (first name was not given). Her son , Alonzo, was the informant for both records. Her birth date is given as May 10, 1850 on these records.
The obituary for Albert Cottrell lists his parents as Hiram and Arminda Vanski Cottrell.
The obituary and death certificate for Viola Detillion lists her parents as Harim and Arminda Vansky Cottrill.
The obituary for Alonzo Cottrill (Coterel on death certificate) lists his parents as Harman and Amanda Cottrill (Coterel)
The obituary for Amzie L. Cottrill lists his parents as Hiram and Arminda Vansky Cottrill.
The obituary and death certificate for Emily Saxton lists her parents as Hiram and Arminda Vanscoy (Vanskoy) Cottrill.
From Pike County, Ohio marriage records:
Coteral, Emma to Henry Saxton on 5 Jan 1915 (Emma's parents listed as Hiram and Armina (Vansky) Coteral)
Coterel, Amizia to Lulu Ada Bauer on 21 Mar 1912 (Amizia's parents listed as Hiram & Stella (Vanscoy) Coterel)
Coterel, Charles Franklin to Sarah Katherine Anderson on 28 Feb 1912 (Charles' parents were listed as Hiram & Arminda (Vansky) Coterel.
Cotterell, Viola to Edward Detillion on 16 Aug 1900 (Viola's parents were listed as Harmon & Lizzie (----) Cotterell).
From Jackson County (Jackson Twp), Ohio birth records
Cotterel, Albert 11-10-1872 Parents: Hiram Cotterel - Arminda Vanski
Cotterel, Eva Jane 8-29-1878 Parents Hiram Cotterel - Arminda Vansky.
Based upon these records, I would say that Arminda's maiden name was Vansky/Vanscoy.
Hiram (Harm) can be found with Arminda on the 1870, 1880, and 1900 census records (Harmon passed away in 1906).
The point of confusion resides in the marriage record between Harmon and Arminda. It is recorded as follows:
Cotterell, Harmon to Arminda Kinnison on 21 Jul 1866 (meaning Arminda was at least 16 at the time of marriage)
I was (have been) unable to find anyone who fits Arminda in the 1850 census for the tricounty area of Ross, Jackson and Pike County.
There is a 5 year old girl living with a Samuel and Elizabeth Kinnison on the 1860 Pike County, Ohio census.
A further check of the Jackson County, Ohio census reveals that an Elizabeth Vanskay was married to a Samuel Kinnison on Dec 8, 1856. However, this marriage occurs approximately 6 1/2 years after Arminda was reported to be born and not quite 4 years before the 1860 census was taken of Samuel and Elizabeth Kinnison. Also, this marriage was less than 10 years before Harmon married Arminda.
This leads me to assume that Arminda was a daughter (or a niece?) of Elizabeth Vanskay and her first husband (or a daughter of one of her deceased brothers). I suppose she (Arminda) could have been born out of wedlock as well. I am pretty convinced that Samuel Kinnison was not her biological father. Although there are no papers to show this, Samuel Kinnison may have adopted Arminda.