Please mark as private - Add a feature slider button - not possible with std theme

Hi

My client would like a feature button adding to their website, in a place where it will really stand out, however I have no room on the menu bar and are not allowed to remove anything from the main menu.

I was wondering if it would be possible to add a button to the first slider image please, which is coming from "Painting" in a blog post. The button needs to link to this page http://goo.gl/j85wmZ.

Not quite sure how this could be done using CSS.

My clients website is http://goo.gl/mAzHiB, please do not mention the client's website in your reply so it doesn't get indexed by google & please mark this question as private.

Many Thanks
Joanne