I would keep the blind working parts and pull off the canvas part. Make a new one from fabric or vinyl or a tablecloth/oil cloth or even wallpaper. If you use fabric it may need to be starched heavy. If you choose to cover the blind with thin fabric and glue it on the existing canvas remember whatever you do don't roll them up for several days in case there's some moisture left also the thicker the fabric you use when rolled up it may not clear the top of the window top or depth where the brackets are attached to the window.
Posted my reply before your picture came up...... I believe I would purchase material and make a new shade...... Doesn't look like paint would cover that and it would take too many coats.... wouldn't hold up, I'm afraid!
My only other suggestion would be to purchase a piece of canvas in the color you want and sew it, or glue it to this shade.
I paint almost anything, (including ceramic tile)and fireplace brick, also glass, but have never painted a canvas roller shade.
If I was going to I would get the kind of paint that is for material (like the spray paint you would use on silk flowers, etc)
The other paints would crack with raising and lowering the shade.
If it is very dark canvas dying it would not work.
There is a spray paint that you can dye carpets with but I have never seen any in the stores.
This would be one project that I would try first on a very inconspicuous spot... let it dry and see what happens.
Good luck!
Thanks, I may have to look into it more, the blind is solar reflective on the back so it is a very heavy.