多说的https支持并不是特别好，尤其是头像跟表情，依然走的http协议，会让你的小绿锁消失，无奈只能本地反代这些头像。
直接上nginx规则，请自行将cdn.run.la替换成你自己的域名，因为我是使用cdn进行缓存的，所以nginx并没有配置缓存。

nginx规则

    resolver                 119.29.29.29 223.5.5.5  valid=600s;
    resolver_timeout         10s;
    location ~ ^/duoshuo/(\w+\.)(t\.sinajs\.cn|bdimg\.com|cdncache\.org|douban\.com|gravatar\.com|qlogo\.cn|sinaimg\.cn|xnimg\.cn)(\/.*)$ {
        proxy_connect_timeout    10s;
        proxy_read_timeout       10s;
        proxy_set_header Host $1$2;
        proxy_pass               http://$1$2$3;
        proxy_http_version 1.1;
        proxy_set_header Connection "";
        expires      30d;
    }

    location /duoshuo/embed.js {
        proxy_connect_timeout    10s;
        proxy_read_timeout       10s;


        sub_filter 'avatarUrl:function(e){return e.avatar_url||rt.data.default_avatar_url}' 'avatarUrl:function(e){var avatar_url=e.avatar_url;if(!avatar_url){if(rt.data.default_avatar_url.indexOf("http:")){rt.data.default_avatar_url=rt.data.default_avatar_url.replace("http:","https:")}return rt.data.default_avatar_url.replace("http:","https:")}else{if(avatar_url.indexOf("qzapp.qlogo.cn")!=-1||avatar_url.indexOf("wx.qlogo.cn")!=-1){return"//cdn.run.la/duoshuo/"+avatar_url.replace("","")}else if(avatar_url.indexOf("q.qlogo.cn")!=-1||avatar_url.indexOf("app.qlogo.cn")!=-1||avatar_url.indexOf("avatar.duoshuo.com")!=-1){return avatar_url.replace("http:","https:")}else{return"//cdn.run.la/duoshuo/"+avatar_url.replace("","")}}}';

        sub_filter 'r=s.author;' 'r=s.author;if(s.message.indexOf("http:")!=-1){s.message=s.message.replace(/src=(["|\'])http:\/\//g,"src=$1//cdn.run.la/duoshuo/")}';

        sub_filter 'S.STATIC_URL+"/images/smilies/"+s;' 'S.STATIC_URL+"/images/smilies/"+s,i=i.replace("http://","//cdn.run.la/duoshuo/");';

        sub_filter_once on;
        sub_filter_types application/x-javascript;

        proxy_set_header Host static.duoshuo.com;
        proxy_set_header Accept-Encoding '';
        proxy_pass               http://static.duoshuo.com/embed.js;
        proxy_http_version 1.1;
        proxy_set_header Connection "";
        expires      30d;
    }

引入embed.js文件

<script src="//cdn.run.la/duoshuo/embed.js" data-no-instant></script>

参考文档

https://imququ.com/post/duoshuo-and-https.html
https://qqdie.com/archives/duoshuoxhttps.html