I am not sure if the Charles Cole I have information about is the Charley Cole you are interested in, but there are some interesting links that might fit.
Charles Cole (May 1876, Ind)was born to my great grandfather's brother, Benton Cole (1842 Ind) and Elizabeth Miller Cole (Dec 1844 or 45, Ohio). The family moved to Utah about 1883. I see them in the 1900 census there. The father, Benton, died in Utah in 1905. I cannot find any of the rest of the family in the 1910 or 1920 censuses. But Charles Cole, born 10 May 1876, registered for WWI draft in Boise listing his nearest relative as Elizabeth Cole.
In 1922, Charles Cole of Boise married Viola Mundy of Portland,in Salt Lake City.
In the 1930-31 Boise Polks' City Directory, Chas Cole (Viola) is listed with his mother Eliz Cole (wid Benton).
The 1930 census in Ada County lists Charles Cole, 48 (1882??), first marr age 20, Ind with Viola I, wife, 38, Id, and mother Elizabeth, 86, Oh.
HERE IS THE REASON I THINK THERE IS A CONNECTION:
The obituary for Elizabeth Cole reports that she died at the home of her daughter in law, Viola Cole, and that she had a surviving granddaughter, MRS VALLIE BURKE and 2 great grandchildren.
I'm thinking that Charles was married previously and is the father of Vallie.