We here at Lead Stories like to be on top of what's trending on the internet. Share counts are an indispensable tool for us to see how popular a post is, so Twitter's announcement that it would remove the share counts from the official Twitter buttons posed something of a problem for us. We don't like problems so we came up with a solution. Enter OpenShareCount.
OpenShareCount will get your counter working again, no matter if you are using Twitter's own default share button or a custom, third-party solution. It uses Twitter's REST API to search for tweets with your links in it and keeps track of the number of results over time. Unfortunately search only goes back a week and it does not cover private accounts. This means the count might not be 100% accurate (especially for older posts) but at least it gives you an idea of the relative popularity of your recent posts.
Greetings from the Lead Stories / OpenShareCount team