🎉 Chrome finally accepts SVG favicons now that crbug.com/294179, where this feature was demanded on September 18, 2013(!), was fixed. This means that you can style your icon with inline prefers-color-scheme and you'll get two icons for the price of one!

<!-- icon.svg -->
<svg width="100" height="100" xmlns="http://www.w3.org/2000/svg">
  <style>
    circle {
      fill: yellow;
      stroke: black;
      stroke-width: 3px;
    }
    @media (prefers-color-scheme: dark) {
      circle {
        fill: black;
        stroke: yellow;
      }
    }
  </style>
  <circle cx="50" cy="50" r="47"/>
</svg>

<!-- index.html -->
<link rel="icon" href="/icon.svg">

You can see a demo of this in action at 🌒 dark-mode-favicon.glitch.me ☀️. Until this feature will have landed in Chrome Stable/Beta/Dev/Canary, be sure to test it with the last Chromium build that you can download from François Beaufort's Chromium Downloader.

Full credits to Mathias Bynens, who independently has created almost the same demo as me that I didn't check, but whose link to Jake Archibald's post SVG & media queries I did follow. Mathias has now filed the follow-up bug crbug.com/1026539 that will improve the favicon update behavior (now you still need to reload the page after a color scheme change).