…or you may change in file wp-shoutbox-live-chat/js/shoutbox-core.js line:
var replace = '<img src="/wp-content/plugins/shoutbox/img/'+Shoutbox['smilies'][smile]+'" alt="'+Shoutbox['smilies'][smile]+'"/>'
with:
var replace = '<img src="/wp-content/plugins/wp-shoutbox-live-chat/img/'+Shoutbox['smilies'][smile]+'" alt="'+Shoutbox['smilies'][smile]+'"/>'
and in file wp-shoutbox-live-chat/js/shoutbox-init.js line:
string += '<div class="shoutbox-smile-container shoutbox-smile" title="'+smile+'"><img src="/wp-content/plugins/shoutbox/img/'+Shoutbox['smilies'][smile]+'" alt="'+Shoutbox['smilies'][smile]+'"/></div>'
with:
string += '<div class="shoutbox-smile-container shoutbox-smile" title="'+smile+'"><img src="/wp-content/plugins/wp-shoutbox-live-chat/img/'+Shoutbox['smilies'][smile]+'" alt="'+Shoutbox['smilies'][smile]+'"/></div>'