I checked on the website of a vendor I know, American Rubber Products,
and they have a variety of nitrile and neoprene coated cotton fabric.
They also state they have very small minimum orders (1 yard or $75).

It's been so long since I worked with the material that I don't know
what thickness is required, so perhaps somebody who's really into it
could check it out.  Just thought I'd pass it along as a possible
source.  Their website is

http://sscrubber.com/home/our-products/rubber-coated-fabrics/ 

Rich Sitler

 [ Shibata manufactures a similar product line, see
 [ https://www.sbt.co.jp/En/products/RRS/rubber_s.html 
 [ -- Robbie