Hi. Sorry it's taken me a bit to get back to you. I've been really busy and not able to get to this until this weekend.
Anyhow, here's what I have come up with based on your information and on other's that was posted on the internet. See what you make of it.
Several people on the internet had Samuel cochran as the father of your Samuel and not William J. i'm not sure which is correct. The William J. Cochran living in Shelby Co., MO in 1840 doesn't quite match up age-wise with the children living with Fanny Cochran in 1850.
Here are those censuses.
1840 shelby co., p. 25
Wm. J. Cochran
1 male under 5, 2 males 5-10, 1 male 10-15, 1 male 30-40 & 1 male 40-50
1 female under 5, 1 female 10-15, 2 females 15-20 & 1 female 40-50
1850 Shelby Co., MO p. 235a
Frances Cochran, 46, VA
James W., 23, KY
Samuel, 19, KY
Frances, 18, MO
1860 Tiger, Shelbyville, Shelby, MO, p.
Samuel Cochran, 28, KY
Sarah, 25, MO
James W., 3
Frances, 5 mo.
1870 Bethel, Shelby, p. 15
Samuel Cochran, 36, KY
Sarah, 35, MO
1880 Rock Creek, Otoe, NE, ed 191, p. 345c
samuel Cochran, 47, farmer, KY/KY/KY
Laura, 36, MO/TN/TN
1900 Elk Pct., Nuckolls, NE, ed 130, p. 5a
Samuel Cochran, 8/1833, 66, married 43 yrs, KY/IRE/MD
Larey E., 8/1844, 55, she has had 3 children, 2 are living, MO/TN/TN
Maggie, 10/1882, 17, NE
Gertie, 9/1884, 15, NE
One of the people who posted about this family said that the parents of Samuel were Samuel Cochran b: 4/22/1775 NC and Frances Fanny Woods b: 5/15/1799 Orange, VA, d: 12/26/1855 Shelby,MO. they were married about 1826 in Madison Co., KY.
Here are the records I have for Madison Co. marriages:
"Samuel Cochran married Fanny Bates, bond date: 19 Jan 1802, bondsman: Thomas Bates, return of bond: 19 Jan 1802"
"Samuel Cochran married Fanny Woods, bond date: 19 Dec 1826, bondsman: James Woods, return of bond: 19 Dec 1826"
Madison Co. Marriages, compiled by Bill and Kathy Vockery
There is a Fanny Cochran buried in Madison Co.
"b: 17 Jul 1772, d: 25 May 1824.
There is only one grave at this site. It is located 1.4 miles west on Menelaus Road from US 25 to a gravel road which runs south near a sharp curve. Take gravel road about .3 miles to old house. stone is in field south of the house." Madison co. Cemetery Records, Vol. II, Southern Section, compiled by Bill and Kathy Vockery
In "Kentuckians in Missouri" by Stuart Seely Sprague there is this from Madison Co., KY:
"birthdate: 03 feb 1828, James W. Cochran, parents: Samuel & Frances (Wood), he b: NC, she ?." The source for this information is from: "History of Monroe and Shelby Counties, Missouri, written and compiled from the most Authentic Official and Private sources, including a History of their townships, towns, and Villages, Together with a condensed History of Missouri...Biographical Sketches of Prominent Citizens...Saint Louis: National Historical Company, 1884, p. 1091"
You might be able to get this book through inter library loan.
Anyhow, it looks like Samuel might be the father of your Samuel.
You might write to the Shelby Co. Courthouse and see if they have a will and/or probate for Samuel Cochran about 1848-1850 and one for Frances about 1855. You might also ask for a marriage between Samuel and Sarah Joyner/Joiner and Samuel and Laura Joyner/Joiner.
If you write be sure to include a SASE so they can respond easily.
I can do a bit more digging if you like.