Force the browsers to download new favicon
Some browsers, Chrome for example, maintain a separate storage to cache favicons because they're frequently used in different places such as bookmarks, history.
When we replace the favicon with a new one, our visitors probably still see the old one, even if they clear the browser cache.
To prevent this from happening, we can always force the browsers to download the new favicon by adding a query parameter:
<link rel="icon" href="/favicon.png?ver=2" />
Of course, it's up to you to pick another name and value of parameter.