stores its favicons in
/usr/syno/synoman/webman/favicon.ico /usr/syno/synoman/webman/resources/images/icon_dsm_16.png /usr/syno/synoman/webman/resources/images/icon_dsm_32.png /usr/syno/synoman/webman/resources/images/icon_dsm_48.png /usr/syno/synoman/webman/resources/images/icon_dsm_64.png /usr/syno/synoman/webman/resources/images/icon_dsm_96.png
Simply replace these files and you're done. If you don't have all the various resolutions, and to be fair some will never be used anyway then remove the files.
Personally, I created a zip file with my favicon.ico in the root, and the remaining icons in resources/images/icon_dsm_… this means that when DSM updates and overwrites these files I can just download the zip file again with curl. e.g. if my server is myservername and I created my zip file as favicons.zip then I'd download it using the command
curl "myservername or ip/favicons.zip" -o favicons.zip
Assuming I downloaded it into /usr/syno/synoman/webman then I would extract and overwrite the favicons with
7z x favicons.ico
You will need to refresh the page in your browser WITHOUT CACHE to see the updated icons. In Safari for example this is ALT+CMD+R. From memory Firefox is CMD+SHIFT+R and so on.