I noticed a comment in another thread that low B (B4) can be played on Coda by "underblowing" low C. That is, if you play low C very gently, it will be a semitone flat and you'll get B. This works, but I think there's a better way.
Instead of reducing your breath pressure, tip Coda down you play low C with normal firm breath pressure. As the low chamber windway approaches your lower lip, the pitch will fall without your having to reduce breath pressure much, if any. It just takes some practice to home in on the bite you want.
On Christmas Eve I played with a small church choir and piano. One of the songs was, of course, "Silent Night." It was scored in Bb, so there was no possibility of playing it in a different key. In Bb it fits nicely on Coda--except for the very last note, the final "heavenly peace." That note is a low Bb, below C.
I knew beforehand that I'd be playing this, but I didn't know if it'd work, so I also brought along a Bb tin whistle, just in case. I was so busy that day I didn't have a chance to practice beforehand except in the car, before going in. So I just tried the low Bb and found I could hit it easily. In fact, I found I could get down to A, but that one did require some reduction in breath pressure, but Bb was fine. So I left the Bb whistle in the car and used Coda for the whole service, except for one song on tenor sax.
Tl;dr You can play down to Bb without much difficulty and without making it so quiet that no one can hear it.
PS On the MO I could and did play down to low A using the same technique, only tipping the instrument up, due to the placement of the windway on top. It's easier than it sounds to describe it.