Unless you are talking Orthophonic and similar where the diaphragm is designed to move like a piston, most diaphragms are designed to be held rigidly and flex across the entire surface. Flexible surrounds would defeat this.
Here is a link to just one of a number of sources for carbon fiber I found on the internet:
http://www.graphitestore.com/cat.asp/spcat_id/2
I still think polymerized paper is a viable alternative for DD and cylinder reproducers. What does a diaphragm need to be?
a) strong
b) dimensionally stable in varying conditions of temp and humidity
c) airtight
d) proper thickness/flexibility/'crispness'
By soaking paper in PEG (which is used by wood workers to stabilize green wood before working it so it will not split after drying) the paper remains paper, but takes on the added desirable characteristics of plastic (see a, b, c & d above). Polymerizing paper is the equivalent of Edison's original method of shellacking rice paper, but likely much superior due to the nature of modern materials.
John M
"All of us have a place in history. Mine is clouds." Richard Brautigan