Funeral home records often contain the same information as death certificates, plus other family information. Some funeral home records have a wealth of information.

To find the name of the funeral home:
Check the death certificate it normally gives the name and city of the funeral home. Locate an obituary they often list the funeral home. Locate where your ancestor is buried then check that county for a list of funeral homes, often families used the same funeral home as previous and future generations did. Funeral homes changed names, merged and a few earlier ones just closed. To find the older records is a challenge.
Sources:
Creek Co. Funeral Homes	More About Oklahoma Vital Records
Funeral Home Records Lookup	Creek County volunteers
Funeral Homes of Oklahoma
Obituaries	Newspapers
Cemeteries	Libraries
SSDI Search	Vital Records