###The no coding, clean hands, solution:

Feeds + [Feeds JSONPath Parser][1]

###Coding, dirty hands, solution:

Using REST with [Webservices][2] you can Get and then Post/Patch. You would also need to comeup with a way to schedule your code so it runs every x amount of time (create a cron job); in contrast, Feeds already has that feature. 


  [1]: https://www.drupal.org/project/feeds_jsonpath_parser
  [2]: https://www.drupal.org/project/services