It sounds like you probably want to add the button to the EasyBlog layout files directly. From there, you can make sure it appears where you want within the content area of a post. In there, you can also do additional PHP checks for if the user is logged in, the original editor and/or the post has been published. Then, you can choose to show the button or choose to hide it.
With all that said, I'd suggest making sure you're using Open Graph Actions appropriately. I'm not sure what action you're trying to post, but ones like "I just published an article", "I just contributed", "I added" would work and should go in the user's own Activity Log and may show up in their Timeline. If you're simply looking for a way to post something back to their feed, you may want to consider the Facebook Like or Share buttons instead.
I hope that helps,
Alex
open graph easy blog
