I'm not 100% sure this is the only way, but we made it work as follows.
First, it is mandatory to have a Chinese account, so ask someone in China (for example your client, or a colleague, which is what I did) to subscribe and fill in the required info. He/she will have to create and retrieve an app key (see below).
Then, add the following script tag anywhere in the page within the <body> tag (I've put it at the bottom for performance's sake):
< script src="http://mat1.gtimg.com/app/openjs/openjs.js#autoboot=no&debug=no"></script>
Please note: there's a whitespace between < and script because SO refuses to post the answer if it contains script tags: don't forget to remove the whitespace if you copy-paste the above code.
Lastly, add the following code where you want the QQ Weibo share button to appear:
<div id="qqwb_share__" data-appkey="YOUR_APP_KEY" data-icon="0" data-counter="1" data-counter_pos="right"
data-content="title" data-richcontent="line1|line2|line3"
data-pic="pic"></div>
You'll have to replace:
title with the title of the page
lineN with a short summary of the page
pic with the URL of an image
these will show up on the shared item.
YOUR_APP_KEY with the numeric app key assigned by QQ Weibo.