Transfer data from local SQL database to remote SQL database without remote access to SQL (PHP)

I have a local database and all tables are defined. Eventually I need to publish my data remotely, which I can easily do with PHPmyadmin. The problem is my remote host doesn't allow remote SQL connections at all, so writing a script that does mysqldump and running it through the client (which would be ideal) won't help me here. Since the schema will not change, but the data will be, I need some kind of PHP client that works "in reverse".

Edit: I want this to be an automated solution, so I don't have to copy / paste the SQL every time I make a change!

My question is if there is such a client and what will be recommended to use (from experience). I just need a one way trip from my local database (Rails) to a remote database (PHP supported), preferable as much as possible and simple. Thanks for your responses, comments and feedback!