IIS will list the certificates under "Server Certificates" from the Local Machine SSL store only if these certificates have a valid private key and are meant for Server Authentication. To fix this problem, try recovering the private key of the SSL certificate.
Recover the Private Key of the SSL Certificate
To recover the private key, you will need to repair the certificate by issuing the following command.
certutil –repairstore my <certificate serial number>
Follow the below steps to obtain the serial number of the certificate.
1. Open IIS manager.
2. Under the Connections pane, select the server name and go to the Server Certificate option.
3. Select the desired certificate, right-click on the certificate name and then select the View option.
4. On the next screen, click on the Details tab. Here, you will see the Serial Number of the certificate.