Rubberized silk was the first material used for shutter curtains starting around 1907. It was .007 inch thick when new.
The rubber will swell, crack and fall off with age depending on storage conditions, sunlight and heat being the biggest contributors to the rubber failure.
Golden Heavy Body Acrylic Artist Paint #1040 Carbon Black
https://www.goldenpaints.com/products/colors/heavy-body diluted up to 1:1 with water or their reducing fluid painted on wilt a fine (economy) artist brush will be light tight in 2 to 3 thin coats.
I have only used it on Graflex Focal Plane Shutters and no extra tension was needed to get the shutter operational.
Ebony fabric paint will work also but on occasion will remain tacky enough to stick to itself.
Check local hobby shops or art supply stores for the Golden paint. Golden Fluid Colors will work but dries a little stiffer.