MainWP Branding Extension allows you to customize your WordPress (child) sites. With the Branding extension you can easily Change the Favicon.
This option provides you ability to replace default WordPress favicon on your child sites. To do that, go to: MainWP Branding Extension settings page, locate the WordPress Branding Options section and the second option in the section will enable you to do this:
Click the Choose File button and locate the image you want to use. If you are done with your WordPress customization, click the Save Settings button at the bottom of the page.