There are more options how to create a favicon with transparent background:
- Draw the favicon online and set the transparent background, for example via https://www.favicon.cc
- Upload your image to https://www.lunapic.com and choose which color has to transparent. Then generate a favicon from modified image via https://www.favicongenerator.com
- Modify the image in grapic editor, for example in Photoshop. Set the transparent color and save the image in ICO format.
In case of the first and second option, the online applications are user friendly, so no graphic editing skills are required.