Not sure if you have Facebook Connect on your site. If not, take a look at this tutorial page on to implement Share button/link. Then you can just stick a <img> tag between the <a></a> with your custom button image. For example:
<a name="fb_share" type="icon" share_url="YOUR_URL"><img src="/img/custombutton.png"></a>. That way your custom button gets displayed with clickable FB link.
If you have Facebook Connect implemented, I'm sure there's a way to customize it too, but I haven't looked into it.
