To get a secure URL you need an SSL Certificate. 
You can add it to a new domain or subdomain.

This will give you a secure website such as

You can add the SSL Certificate in the CPanel. 

Inside Cpanel Click:

Find any domain or subdomain that has the red icon:

Then Run The SSL By Clicking This Button Below:

***After you click it will run for a bit.  When it is finished the red icon will be gone.
Then check your domain or subdomain by entering "https://" before the domain
and check it in your browswer.