Mapping to Domain
Your site must be published to a sites.google.com URL before it can be mapped to a domain.
You can use a custom domain for a site published on new Google Sites.
Enter a site name in the 'Web address' box. Use only lowercase letters, numbers and dashes. Your site URL will appear below the box. Do NOT enter the domain!
If you want to use a custom domain that you own click Manage.
Alternately you can just publish the site and set up the custom domain later.
If you want a domain link that goes to a particular page in your site, use forwarding instead of mapping. For instance rate.k8oms.net
I did this by setting up forwarding in my domain panel to forward the subdomain 'rate' to a page in the site. See the image below to see how I did it in Godaddy.
New Google sites are automatically secure (https) at the native Google URL and at the mapped domain, so it is not necessary to purchase a SSL certificate. If necessary, use this procedure to refresh the certificate: Remove the custom URL from your site, wait about 15 minutes then add the custom URL again and that will generate a new SSL certificate.
I don't see custom domains option
There are 2 reasons that you cannot see the custom domain option in Google Sites: