I checked the 1850 census and found the following:
Illinois, Pike, Twp, 6 S 2 W, Image 20
Levi Kinnan 27 Farmer Missouri Mary J. Kinnan 23 Illinois Elisabeth A. Kinnan 3 Illinois James H. Kinnan 1 Illinois
Although Mary J's age appears the same in both census years, I suspect that this is the family you are searching for.
I also found the following marriage record:
Elihu S. Kinman - Mary J. Evans - 9 Feb 1840 Brown Co., IL
And in 1863, Mary J. Kinman remarried:
Abel B. York - (Mrs.) Mary J. Kinman - 22 Nov 1863 Pike Co.
In the 1840 census there are 2 families in Brown county with the surname Evans, but only 1 family with a female that is the correct age for Mary J.
William Evans and family are also in the 1830 census in Brown Co. AND while I was unable to find the family in the 1820 census, there is a Land transaction that took place in 1818 with William Evans as the purchaser.
I hope you find this helpful and I wish you the very best of luck with your continued research.