Enabling breaking news notifications on Sierra
Try this!

[macOS Sierra v10.12.1  &amp;  Safari v10.0.1]


Navigate to Safari>Preferences
Make sure Safari Push Notifications are enabled at the bottom of the Notifications Pane
Delete Safari Caches and make sure Cookies and Website Data are enabled in the Privacy Plane

-You may be able to get away with just deleting "nytimes.com"





Make sure JavaScript is Enabled in the Security Pane
Restart Safari and surf to nytimes.com




Please let me know if you still have any trouble!