One idea that might be worth pursuing is Elias Benjamin Blunt and Elizabeth Manning. They moved from LA to TX and are on the 1860 Census (last name listed as Bluntt) living in Tyler, TX with six children. There is a daughter C.A. who would be about the right age and was born in TX. There is another daughter Delia, but two daughters with rhyming names may just be coincidence.
The entire family record just disappears after 1860. Maybe C.A. Blunt and Cecilia A. Blunt are the same person.
I've seen other trees that indicate her parents were John Thomas Blount and Clarissa Ann Cartwright, but that is not correct. John Thomas is in my line and his daughter was Clarinda Texas Blount.