Elliott Co., Ky birth records list Benjamin L. Binion, born 10 Oct 1875, father Lincoln Binion, mother’s maiden name Louisa Porter.

1910 census of Elliott Co., Ky, Laurel precinct, enumerated 29 April, lists on p. 9A as family #147/150:
Binion, Luster, 41, farmer; Sarah, wife, 37; Martha, dau, 15; John, son, 14; Leander, son, 12; Causby, dau, 9. All born Ky Ky Ky.

I’m very skeptical that this is the family of Luster Binion and Sarah Flannery, since the child lists do not match at all, and the ages for Luster and Sarah are inconsistent with other records as well. But I cannot find any other Luster Binion (or variant spelling) in 1910, nor any Binion family with children John or Riley about 4 and/or Hazel about 2 or Myrtle age 1 in 1910, in a statewide search. I also cannot find a match for the family above in 1900 or 1920.

There is a death certificate for a Sara Binion who died 3 June 1912 in Laurel precinct, Elliiott Co., Ky, listed as married, age 26 years 10 days, born 24 May 1886 in Kentucky, father William Flanery, mother’s maiden name Mary Flornry (? possibly intended as Flanery), cause of death blank, informant Andy Porter.

The reported birthdate does not match at all with the wife Sarah listed with Luster Binion in the 1910 census, but the date of death would fit well with when Luster remarried to Delphia Skaggs, and the 1910 census reading is either for the wrong Luster Binion family or very badly mangled.