JDownloader provides several Addons. How to install and update the addons is explained here
The addon called „RemoteControl“ allows you to control remotely your JDownloader-client by doing so-called HTTP-requests. In doing so you execute commands which are nothing else than URLs that will be called over the network-protocol HTTP. This can be done by simply typing them into the address-bar of a webbrowser or by (and that's why this addon was made) other applications and scripts that can handle HTTP-requests.
You can download the demo here: Externer Link
A propper remote-API will probably come some day but until it's done the „new old“ „RemoteControl“ will do the job quite well, I think.