Unfortunately it is always harder to find documentation for more recent events because of privacy issues.I did find an obituary (The Advertiser 12/27/2007, Lafayette) for a child of Cecil/Clara (Elizabeth "Betty" Jett Sunday, born 9/21/1937 Louisiana) and had lived in Lafayette for 50 years.Obit also states she will be interred next to her parents in Calvary Cemetery.You can view this obit in full at the WWW.MOURNING.COM.Input death date 12/21/2007.
This would lead one to assume a sister born in 1939 would also have been born in Louisiana... probably Lafayette County. The following website will tell you how to order birth records in Louisiana. http://www.dhh.louisiana.gov/offices/page.asp?id=252&detail=7752http://www.dhh.louisiana.gov/offices/page.asp?id=252&detail=7752
Since Clara Belle Fleming was raised in Vermilion County it is quite probable she married there as well.Try the following to get marriage record information.