[EDIT]: Sorry, jumped the gun a bit. Since this is a cPanel server, a subdomain is added as a subdirectory in your main domain's document root. You should also edit your existing robots.txt of your main domain to exclude this subdirectory, in addition to the new robots.txt for your subdomain.
So if secure.example.com is in a subdirectory named "secure":
Thank you, for all of the information you provided. I am going to add a robots.txt file to the "secure" subdomain and also will add the lines you suggested to the existing robots.txt file. Much appreciated! Lanny