Now based on Alpine Linux and s6 as supervisor, resulting in a much smaller Docker image. See README.md for details and other additions.

root/etc/cont-init.d/99-ttrss

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+#!/usr/bin/with-contenv sh
+cd /srv && ./setup-ttrss.sh

root/etc/nginx/nginx.conf

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+user www-data;
+worker_processes auto;
+pid /tmp/nginx.pid;
+daemon off;
+
+events {
+    worker_connections 1024;
+    use epoll;
+}
+
+http {
+    include /etc/nginx/mime.types;
+    default_type application/octet-stream;
+
+    access_log /var/log/nginx/access.log;
+    error_log /var/log/nginx/error.log debug;
+
+    sendfile on;
+    keepalive_timeout 15;
+    keepalive_disable msie6;
+    keepalive_requests 100;
+    tcp_nopush on;
+    tcp_nodelay on;
+    server_tokens off;
+    
+    fastcgi_temp_path /tmp/fastcgi 1 2;
+    client_body_temp_path /tmp/client_body 1 2;
+    proxy_temp_path /tmp/proxy 1 2;
+    uwsgi_temp_path /tmp/uwsgi 1 2;
+    scgi_temp_path /tmp/scgi 1 2;
+
+    gzip off;
+
+    server 
+    {
+        listen                    4443;
+        root                      /var/www/ttrss;
+
+        ssl                       on;
+        ssl_certificate           /etc/ssl/certs/ttrss.crt;
+        ssl_certificate_key       /etc/ssl/private/ttrss.key;
+        ssl_protocols             TLSv1 TLSv1.1 TLSv1.2;
+        ssl_prefer_server_ciphers on;
+        ssl_ciphers               "ECDHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-AES256-GCM-SHA384:DHE-RSA-AES128-GCM-SHA256:DHE-DSS-AES128-GCM-SHA256:kEDH+AESGCM:ECDHE-RSA-AES128-SHA256:ECDHE-ECDSA-AES128-SHA256:ECDHE-RSA-AES128-SHA:ECDHE-ECDSA-AES128-SHA:ECDHE-RSA-AES256-SHA384:ECDHE-ECDSA-AES256-SHA384:ECDHE-RSA-AES256-SHA:ECDHE-ECDSA-AES256-SHA:DHE-RSA-AES128-SHA256:DHE-RSA-AES128-SHA:DHE-DSS-AES128-SHA256:DHE-RSA-AES256-SHA256:DHE-DSS-AES256-SHA:DHE-RSA-AES256-SHA:AES128-GCM-SHA256:AES256-GCM-SHA384:AES128-SHA256:AES256-SHA256:AES128-SHA:AES256-SHA:AES:CAMELLIA:DES-CBC3-SHA:!aNULL:!eNULL:!EXPORT:!DES:!RC4:!MD5:!PSK:!aECDH:!EDH-DSS-DES-CBC3-SHA:!EDH-RSA-DES-CBC3-SHA:!KRB5-DES-CBC3-SHA";
+
+        index index.php index.html;
+        client_max_body_size 100M;
+
+        location / {
+            try_files $uri $uri/ =404;
+        }
+
+        location ~ \.php$ {
+            fastcgi_split_path_info ^(.*\.php)(/.*)?$;
+            fastcgi_pass unix:/tmp/php-fpm.sock;
+            fastcgi_index index.php;
+            include fastcgi_params;
+            fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
+            fastcgi_intercept_errors off;
+            fastcgi_buffer_size 16k;
+            fastcgi_buffers 4 16k;
+        }
+
+        location ~ /\.ht {
+            deny all;
+        }
+
+        location ~ \.php$ {
+            fastcgi_split_path_info ^(.+\.php)(/.+)$;
+            fastcgi_pass unix:/tmp/php-fpm.sock;
+            fastcgi_index index.php;
+            include fastcgi_params;
+        }
+    }
+}

root/etc/php5/php-fpm.conf

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+[global]
+daemonize = no
+
+[www]
+user = www-data
+listen.owner = www-data
+listen.group = www-data
+listen = /tmp/php-fpm.sock
+pm = dynamic
+pm.max_children = 15
+pm.start_servers = 2
+pm.min_spare_servers = 1
+pm.max_spare_servers = 6
+chdir = /var/www/ttrss/
+request_terminate_timeout = 0
+env[PATH] = /usr/local/bin:/usr/bin:/bin
+php_admin_value[max_execution_time] = 10800
+php_admin_value[max_input_time] = 3600
+php_admin_value[expose_php] = Off

root/etc/services.d/.s6-svscan/finish

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+#!/bin/sh
+
+exit 0

root/etc/services.d/nginx/run

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+#!/bin/sh
+exec nginx

root/etc/services.d/php/run

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+#!/bin/sh
+exec php-fpm

root/etc/services.d/ttrss-daemon/run

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+#!/bin/sh
+
+while true; do
+  cd /var/www/ttrss
+  php -f /var/www/ttrss/update_daemon2.php
+  sleep 5m
+done

root/etc/services.d/ttrss-updater/run

@@ -0,0 +1,6 @@
+#!/bin/sh
+
+while true; do
+  /srv/update-ttrss.sh
+  sleep 24h
+done