You can do this with the site_block template.

Here an example:

Replace in the HTML part:

 <h1>{$insert['block_name']}</h1>

with:

 <h1><img src="https://www.contentteller.com/images/{$block_image}" alt="" /> {$insert['block_name']}</h1>

and add the following PHP part:

$block_image = "default.gif";



if ( $insert['block_name'] == "News" )

{

    $block_image = "news.gif";

}

elseif ( $insert['block_name'] == "Content" )

{

    $block_image = "content.gif";

}

elseif ( $insert['block_name'] == "Knowledgebase" )

{

    $block_image = "knowledgebase.gif";

}

This small script change the block icon image based on the block title. For example, the news block will use images/news.gif as block icon etc.