We have a back in stock notification feature where customers can subscribe to a list so that they can be notified once a product comes back in stock.
Is there a way that when we update a product from "out of stock" to "in stock" we can send a API call to trigger a campaign to start?
If you are using normal email campaigns, you can absolutely trigger an existing email campaign to be sent with the API. You can read more about the scheduling API here: http://developer.constantcontact.com/docs/campaign-scheduling/campaign-schedule-collection.html?meth...
If you are working with Autoresponders, they cannot be managed via the API at this time. We do hope to include this as a feature in a future version of the API, but I do not yet have a time-line for when that would be available.
Please let me know if you have any questions that I can help with!