I'm afraid that's not possible through the API either. A notification is being triggered by a sensor's notification triggers and those triggers cannot be paused. You could pause the notification itself, but that will render the notification then useless on all sensors that trigger the same notification. The only way would be then to pause the sensor itself or you create a dedicated notification in "Setup | Account Settings | Notifications" that you can use then only for this sensor, so that pausing its triggered notification only pauses it for this sensor then.
Disclaimer: The information in the Paessler Knowledge Base comes without warranty of any kind. Use at your own risk. Before applying any instructions please exercise proper system administrator housekeeping. You must make sure that a proper backup of all your data is available.