I had to Google it too.  I found this:  http://www.zuka-chess-opening.net/resources/g6Intro.pdf And then updated my prior post.   

It’s a known limitation.  Different authors have recommended different approaches:

Aaron Summerscale (A Killer Chess Opening Repertoire), Sverre Johnsen  (who updated the Summerscale book) and Richard Palliser (Starting Out d-Pawn Attacks) all recommend the Barry Attack/Pirc.

There is also a related opening called the Tarzan Attack, which has been played by Artur Kogan.

In the Ultimate Colle, Gary Lane suggests a set up similar to the C-Z with d4, Nf3, e3, Be2, b3 and Bb2.  White avoids Bd3, which might run into Black’s ..e7-..e5-..e4 idea.

Keep it Simple does not recommend the C-Z, but Christof Sielecki suggests a double fianchetto system:  d4, Nf3, g3, Bg2, b3, Bb2, which might work for you.  The KID chapter is available as part of the free sample pages.

Finally, there was an amateur player who recommended something he called Zuka.  The basic set up was d4, Nf3, c4, e3, Nc3, Be2.

I've been playing the Colle-Zukertort for a while now and have beaten accomplished players with it. However I always find White's position difficult when Black decides to do a fianchetto on the kingside.

The reason is that the point of the Zukertort is to dominate the diagonal using the bishop, however this domination is put into question when black fianchetto's.

What should my plan be in such a case? Or is this a known limitation to the Colle-Zukertort system?