If you use a plugin like WP Bit.ly or YOURLS to customize shortlinks on your site, Publicize will use your custom short URLs.
If you want to add these shortlinks to the sharing buttons, you can use this plugin:
http://wordpress.org/extend/plugins/jetpack-shortlinks-for-sharing-buttons/
But there is no custom URL plugin for CoinURL. However, I do have a PHP code snippet that changes all URLs on a page to CoinURL links, and an API. Will this help?
The API should allow you to create a small plugin that will generate a short URL for each post, and hook into the get_shortlink filter. All WordPress shortlinks will then be replaced by your own custom shortlinks.
You can have a look at the code of the 2 plugins I mentioned to get an idea of how to implement this.
