To update the webalizer for the single domain refer the following steps, for your kind information if domlogs are rotated on the server then it could be possible that you will miss the existing stats therefore run the command after taking all the essential files backups.
root@server [~]#/usr/local/cpanel/3rdparty/bin/webalizer /usr/local/apache/domlogs/DomainName -n DomainName
For example we are runnning the webalizer for the theperfectarts.com domain
root@server [~]#/usr/local/cpanel/3rdparty/bin/webalizer /usr/local/apache/domlogs/theperfectarts.com -n theperfectarts.com
Once above command run successfuly run the following command
root@server [~]#/usr/local/cpanel/startup