The 1910 Census of Safford, Graham County, Arizona
C.M. Kirkland, age 40(1869/1870), born in Texas to both parents born in Tennessee, living from his own income (no employment type identified), was renting. This was his second marriage of 1 year.
Eva Z, wife, 34(probably 34, 1874/1876), born in Texas to father born in Tennessee, mother in Texas, mother of 1/1 living.
Ethel Gray, age 13(1896/1897), born in Oklahoma to both parents born in Texas.
--Census mistakes on age and places of birth are enough to not trust this as being accurate. Ethel's parents place of birth could be the common era of showing the place of birth of the two above her and not the true place of birth of her real father.
-this census was enumerated on 25 April 1910, so, as you indicate they could have been married anytime after 25 April from 1908.

The 1920 Census of Chickasha, Grady Co, OK
(If this was the one you identified)
C.M. Kirklin (as written and transcribed), age 55, born in Texas to both parents born in Tennessee. Widower. Living as a farm laborer, in the home of the C.T. Taylor Family. C.T, 28, born in Missouri; Pauline, 27, born in TX

FamilySearch.org:
Ethel Gray, was born 29 Sep 1896 in Burnette (there is a Burnett in Pottawatomie County), OK, mother: Eva Kirkland. Ethel married James C. Walker on 18 Feb 1913 in El Paso, TX. James, born Cloudcroft, N.M. age of 24 at the time of marriage (1888/1889), died on 5 Mar 1924 in Otero County, New Mexico, spouse name: Ethel B. Walker.
--in 1901, a Wilburn Gray obtained 160 acres of land in Pottawatomie County. Indian Meridian, Township 6 North, Range 4 East, Section 25, the SW Quarter. This is near the "Gray Oil Field." ("probably the one found in the 1910 Census in Avoca, Pottawatomie, married to Laura with several children, born about 1853 in Arkansas). Probably NOT connected to Eva by marriage.
There were only four "Wilburn" in the 1900 Census, amazingly all had a mother "Eva."

Marriage records in Graham County, AZ:
http://www.graham.az.gov/Graham_CMS/Clerk.aspx?id=420

Between your information and the family tree posted by the other, I don't see proof this was the same person. You or they might have the proof of the connection, but there were MANY having the same names.