I've been posting to a lot of REST services from my Clover projects so hopefully I can assist.
If you have the JSON write to a port, you should be able to send it as input to a Reformat object that has the HTTPConnector_Request as its output metadata.
Then, map the JSON to the requestContent of the output. (If you have any other dynamic content for your HTTPConnector_Request you can configure it in this Reformat as well. For example, I create the URL dynamically using job parameters.)
In the HTTPConnector_Request you can set the HTTP action as PUT, POST etc. as needed and set the URL that you are posting to.
Then in the Input Mapping you can drag the requestContent from the request to the HTTPConnector's requestContent (and set any other parameters you configured in the Reformat and mapped to the HTTPConnector_Request.
I hope that helps you figure it out!