Once a year, our certificates expire for ssl on reporting services.  These can be replaced with zero down time in reporting services.
1.    Every year, the certificate for reporting services must be renewed.
2.    Obtain certificate .pfx file and password from web infrastructure team.
3.    Connect remotely to the reporting server.
4.    Open Control Panel > Administrative Tools > Public Key Management
5.    Open Certificates (Local Computer) > Personal
6.    All Tasks > Import
7.    Let the wizard determine the store.
8.    Open IIS > Web Sites > Default WebSite > Directory Security Tab > Server Certificate
9.    Replace the current certificate
10.    Pick new cert from the store
11.    View the website and click the lock to the right of the url bar in IE.  Click the ‘view certificate’ button and ensure the date has been changed to the new certificate effective/expiry dates.

As you can see, we didn’t restart the website and you’re using the new cert.