Like Box module is likely loading in Facebook JS API which isn't necessary. All you need is the HTML5 source and not the script. For example place the below in a Custom Joomla module (allows HTML) and ensure CBs login module is rendered on all pages and you'll have a working like box. Aside from that there's no workaround as 3rd party Facebook integrations often are including Facebooks JS API which will cause 1 or the other to stop working properly.

With the above you'll need to supply the PAGE_URL to the page you want likes displayed from.

You can find more on social plugins below. Please note CB Connect, which as a professional subscriber you have access to, provides Facebook integration and a new social plugin fieldtype allowing easy creation of Facebook Social Plugins as CB Fields.

developers.facebook.com/docs/plugins/