It is easy and Free :-)
1) Create Facebook App at developers.facebook.com. If you do not know how to do it. Search Google for "How to create Facebook Aps."
2) Go to Dolphin 7.x Admin Panel Tools> Language Settings and edit the following key:
_login_form_description2join (System)
3) Insert the following code after <div class="usualHeader"> and "before Not a member yet?"
<p><a href="http://www.mydomain.com/modules/?r=facebook_connect/login_form">
<img height="20" src="{0}/images/fbc.gif" width="160"></a></p><br />
4) Search for a GIF, JPG, or PNG Facebook Connect picture on Google and save it under Dolphin /images directory. If you do not have /images directory create it. I am using fcb.gif (Do not forget to replace it with the name of you Facebook Connect picture.
Have fun.
See example in action at http://www.shaadiconnections.com