How to pronounce "favicon"?

I usually pronounce it /fav-eye-con/ or /fav-ih-con/, but I've never heard anyone else pronounce it (at all).

Consensus also seems to be /fav-ih-con/:

• http://www.macmillandictionary.com/pronunciation/american/favicon
• http://www.forvo.com/word/favicon/

I definitely say "fav-ick-on", the a like in family. I guess the emphasis is on the first syllable, but it's slight.

As this is a recently coined word I don't think you're going to find a canonical answer yet. This is good, because it means YOU get a chance to contribute to the language by promoting YOUR favorite pronunciation until there's finally a widely accepted norm!