I don't know how much I can provide that you don't know, but maybe I can help with some dates.
In 1920 Viola, Sedgwick, Kansas, George W. Boyer, age 69 born PA PA IRELAND is listed with his wife Nellie, age 37 KS MI NJ. The children are Clara 16, James 15, Laura 12, Mary 10, and Ethel 2.All of the children were born in Oklahoma.Also living with them is Neal Allen, age 22, a boarder.He is also born in Oklahoma, but parents are from PA and NJ.It would appear that George was born about 1851, and Nellie about 1883.
Oklahoma didn't become a state until 1907 so that makes it a little harder.I searched several areas but couldn't find your Boyers.If you knew where even one child was born, it would help.
In 1930 the other child you mentioned, Cornelius,that isn't in the home in 1920, is a ten year old in the home of Olath and Laura Campbell and their 1 7/12 son Kenneth. Cornelius is shown as the brother-in-law.
Since Nellie was born in KS about 1883, I went to my 1880 census CDs and looked for a Cornelius J. Allen born in Michigan. I found one born in Michigan in 1852, but living in Osage, Allen, Kansas in 1880.He was single at the time.
I can also see a George Boyer, age 28, living in Clear Creek, Pottawatomia, Kansas.He is single at the time and listed as a laborer in the home of Adna Inglebee.
I think that I can provide you with the family of Cornelius, if you will write to me.Carol