En donde 123 es el ID del posts a modificar

RESTAPI_modificacion_entrada.php

<?php

$host = 'http://tudominio.com/wp-json/wp/v2/posts/123';

$data = array('title' => 'Titulo Post Nuevo Modif', 'content' => 'Contenido de prueba Modif', 'status' => 'publish');
$data_string = json_encode($data);

$headers = array(
    'Content-Type:application/json',
    'Content-Length: ' . strlen($data_string),
    'Authorization: Basic '. base64_encode('admin:clave')
);

$ch = curl_init($host);
curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, 'POST');  
curl_setopt($ch, CURLOPT_POSTFIELDS, $data_string);
curl_setopt($ch, CURLOPT_RETURNTRANSFER,1);

$result = curl_exec($ch);
curl_close($ch);  
echo($result);