While you can’t yet set a separate image from your profile for your publishing site, you can use this CSS hack to override the default image.  In the “Customize Publishing Site” settings, add this to the “Footer HTML.”  Replace the image url with yours.

<style>
.avatar-box {
background-image: url(//liberty.me/wp-content/uploads/2014/05/liberty.me-bird-logo-white.png);
background-size: 100% 100%;}.avatar {display: none;}
</style>