This is exactly the kind of question that SUSHI-Lite was designed to answer. It provides a RESTful API for fetching COUNTER statistics on-demand.
If you are at OJS 2.4.8 or better, there is a SUSHI-Lite plugin available:
We use this plugin to allow a third-party (Plum Analytics) to harvest COUNTER-ready statistics from OJS for display in a widget that shows on the article abstract page.
A similar plugin could be developed to display just a widget with a professional display of the COUNTER-ready statistics.
For alternate approaches to this, check out this thread: