I have never tried to post with out using cURL as it simplifies the process. You can find more information about HTTP requests on php.net. The documentation can be found here.
Let me know if this helps.
Making an HTTPS request without cURL in PHP is actually a very difficult programming excercise. A long time Constant Contact partner and developer on our API platform actually created a PHP 4.3+ wrapper for our API that you can find here: http://marketplace.constantcontact.com/Listing/applications/justphp/PML-0171
Unfortunately, since PHP 4.x is no longer supported by PHP.net, we are not planning on supplying any examples in that language.