A one time thing or are you needing some sort of HTTP request API? For a one time export you can use phpmyadmin and format the query however you're needing then export it. As for an HTTP request API we have none and best I can suggest is trying to use CB Auto Actions with Triggers set to None and in a Code action write the PHP to do whatever you're needing. You can then access it using its URL under the global tab. Realistically you'll need to develop a custom solution to meet your needs as you're going to have security issues to be worried about, authentication, etc..

Have You experience with JSON Export Joocode joomla extension?

Nope.

Do You think is CB compatible?

No idea.

You can use a Code action to do this I suppose, but like I said you still will have to write code. The initial setup and usage would be as follows.

Global
Triggers: None
Type: Code
User: Automatic
Access: Everybody
Action
Method: PHP
Code:Return: Echo

What $data you output is entirely up to you. There's no security to this endpoint so you may want to add a condition like the following.

[get_key] Equal To YOUR_SECRET_KEY_HERE

This ensures the URL must contain whatever key you want (e.g. f24sg56#$%sfd) or the action won't execute.

You can execute the action directly using its URL found under the Global tab as "Internal Action URL". For JSON usage you'll need to add &format=raw to the URL.

As far as what you need to do in CB the above is it. The code however you'd need to write your self using PHP to output whatever information you're wanting. There's a few PHP tutorials below.

www.w3schools.com/php/default.asp

There's several other sites available for learning PHP in addition to the above around the web.