To specify the image you want used when the Like is clicked, you need to use Open Graph tags. Open Graph integration in JFBConnect is enabled by default, but you can check the setting in the Social Configuration -> Open Graph tab. Then, all you need to do is add the following tag to your article to specify the image you want used:
{JFBCGraph image=http://site.com/link-to-image.jpg}
It will take Facebook 24-48 hours to update the image for new like's, so if you try right away, you may not see a difference. You can use the debug tool to see what Facebook 'sees' on your page from the Open Graph tags:
developers.facebook.com/tools/debug
Finally, you can also use the Open Graph tab in the social configuration area to specify a default image, in case you haven't explicitly set one on a page using the tag above. This is good for using your logo or something, just to make sure some random image isn't shown. To do so, add the following tag into the defaults box:
image=http://site.com/good-default-image.jpg
Hope that helps,
Alex