Google Sites Custom URL
Log into the DNS provider for the custom domain
Add a cname record to for the subdomain with destination ghs.googlehosted.com
Go to admin.google.com > Apps > Core Services > Sites
Click Custom URL
Click +
Click Continue
Enter the native Google Sites URL
Click Continue
Enter the desired subdomain
Click Add Custom URL
Refresh the page every minute until a green check appears under Status
If the custom URL throws Connection Reset errors, check google.com/webmasters/verification/home and unverify the custom domain if it appears there.