This is really late, but if you have not yet found it the Shelby Co Tn deaths are online from a very early uninformative date at the Register of Deeds site

http://register.shelby.tn.us/

It also hold whole state deaths but without the actual image that you can get for Shelby Co. A real treasure trove since many from Mississippi went to Memphis for hospital treatment.
Below are the records held on the site.
Tennessee Vital Records
Death Records Index 1949-2009
Divorce Records Index 1980-2009
Marriage Records Index 1980-2009

Shelby County Records
Birth Records 1874-1906
Chancery Court Divorce Index 1945-1997
Circuit Court Indexes 1893-2000
Death Records 1848-1960
Marriage Indexes/Images 1920-1989
Marriage Records 1820-1970
Memphis Census 1865
Memphis City Directories 1859-1918
Naturalization Records 1856-1906
Probate Court Loose Paper Index 1820-1900
Probate Court Will Book Indexes 1830 to 1955