Users often ask how to set the canonical URL for their Site.
Product Expert Rotary Steve provided this excellent guidance in answer to one such question:
"New Google Sites does not provide a canonical link element for the pages or any other way to explicitly declare what you want the canonical to be.
Pretty much all that can be done is to make sure the external linking (backlinks), goes to the custom domain. If you have other sites that link to your site, be sure that they point to the custom domain and not the sites.google.com/ url.
I would submit some, if not all of the custom domain's pages to Google, see Ask Google to recrawl your URL's/Request Indexing. Not being able to declare a canonical in the New Sites can be a bit problematic, though Google may take favor of the new domain instead of the Google Sites url's.
Google needs as many signals as possible as to what you wish the canonical to be, though regardless Google will always choose what it thinks deserves being declared as the canonical, even if we did have the ability to explicitly declare a canonical form."