So as far as Delilah, we're back to the only Delilah I've noticed so far, already named above as daughter of William Stouffer born 1861 (son of Samuel M. Stouffer 1826-1908)
This Delilah seems to have been about six years old when her parents were married, according to the 1900 census. In her birth record (as found on Family Search) she has been given her mother's surname (again, if we've correctly identified her).Certainly the 1900 census says Elizabeth has had 5 children, and 5 are living, and she and William have been married 1 year. So perhaps the children in that census are not Elizabeth's from a previous marriage, but belong to William and Elizabeth, who married belatedly (by traditional standards). That situation might lead to a birth record not being filed, and Delilah asking for a birth record in later years. Just an idea....See if it fits your Delilah's story.
BIRTH RECORD Delilah Cathern Stouffer Wolfe Born 15 Dec 1893 in Adrian, Armstrong, Pennsylvania Father: William Wylie Stouffer Mother: Synthie Elizabeth Wolfe
1900 Census Armstrong County, Pennsylvania William Stouffer 39, born Dec. 1861 in PA, married 1 year (Occ. day laborer) Elizabeth b. Jan. 1868 in PA. b. in PA. had 5 children 5 living Margie b. Jan. 1890 in PA. Harry b. Nov. 1891 in PA. Deliah C. b. Dec. 1893 in PA. Chester b. Apr. 1896 in PA. William b. Apr. 1899 in PA.