Create two way syncronization between scheduling application and 3rd party application through REST interface

Create an interface between two scheduling applications to syncronize their schedules. One application is a custom application we've developed and the 2nd is a 3rd party application that implements a RESTful API using WebAPI. Any time a new appointment is made in the custom application, it should be posted to the 3rd party application. The code should look for new appointments and changed appointments on the 3rd party application on a regular basis (i.e. every 5 minutes) and if found, update the schedule of the custom application. None of the original code of the custom application should be modified. Ideally the code should be written using a Provider pattern so other 3rd party applications can be used as well. Documentation on the 3rd party application will be provided on project acceptance and a run through of the custom application will be provided to bring the developer up to speed.