From the record below, it appears this couple died within days of each other. The actual certificate is not online. I would contact the Town Clerk in Adger, Jefferson, Alabama to see if you can get copies of the actual certicates as they may have the place of burial or other clues to help your search.
Alabama, Deaths, 1908-1974
Citing the Record: "Alabama, Deaths, 1908-1974," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/JKQM-YBS), Mary E Walden in entry for William C. Walden, 11 May 1918; citing reference cn 99, Department of Health, Montgomery; FHL microfilm 1908199.
Name: William C. Walden
Death : 11 May 1918 Adger, Jefferson, Alabama
Age : 82y 3m 8d
Birth (Est): 1836
Spouse: Mary E Walden
Father: Richard Walden Mother: Lucenda House
Cert. No. 99
Citing this Record: "Alabama, Deaths, 1908-1974," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/JKQM-YYP : accessed 26 Jul 2014), Mary Elizibeth Walden, 16 May 1918; citing reference cn 96, Department of Health, Montgomery; FHL microfilm 1908199.
Name: Mary Elizibeth Walden
Death: 16 May 1918 Adger, Jefferson, Alabama
Age ): 79y 2m
Birth (Est): 1839
Name: William C. Walden
Father: Don'T Know
Mother: Don'T Know
Cert. No. 96