Question : single site multiple hosts

Is there any way to have a backup of my website with shared hosting?  What im looking for is a way to have 100% uptime.  My hosting company does a pretty good job, but sometime their servers go down and my site goes offline.

Is there any way to set up a backup site on a different server and have the customers divert to this if the main site is not online.  Like maybe a mirror of the site on a different server?

my current site is on shared hosting with cpanel, not a dedicated server.  So i do not have SSH access to the server.

Answer : single site multiple hosts

There are several ways to this, you can either use DNS, such as a Cisco Distributed Director, that will act as the nameserver for your site, if it cannot contact your primary site it will redirect to your secondary site.
You can just use a load balancer, this will direct users to one of your backend sites, this can either be a device or a simple linux server running something like keepalived

However in both cases its an external system that could fail.

You will also have to ensure that your two systems are kept up to date, something like rsync.

You may consider putting your secondary site in a cloud such as Amazon