When you say the King's Fianchetto, are you talking Benko's Opening, 1.g3, or do you truly mean the Opening called the Kingside Fianchetto, which is 1.d4, 2.Nf3, 3.g3, and 4.Bg2 WITHOUT c4. With c4, you are in Fianchetto King's Indian and Catalan territory.
The Kingside Fianchetto is an actual opening in and of itself where White plays d4, c3, and fianchettos the kingside.
So you need to be more specific about what you are asking.
What are some strong counter moves for black against this opening? Are there any good ways to counter it with a king's pawn opening?