You were on the right track. IrfanView sets the background for transparency the same as the viewing color around the image. You just need to re-open the image with IrfanView after changing the view color to white. To change the viewing color in Irfanview go to:
Transparency is a property outside the color itself, and it’s also known as alpha component. You can’t code transparency as pure RGB (which stands for red-green-blue channels), but you can use the RGBA notation, in which you define the color + alpha channel together: If you want “transparent”, just set the last number to 0, … Read more
Try http://en.faviconico.org/ online favicon converter. I used this site to convert PNG file into favicon, and the favicon file is still with transparent background.
You can use “transparent” as a colour. In some versions of IE, that comes up as black, but I’ve not tested it out since the IE6 days. http://www.researchkitchen.de/blog/archives/css-bordercolor-transparent.php