Haven't done it myself but have heard of people painting Sunbrella.
Whenever I spill paint
on my paints it ruins them because it never comes off! Artist's paint
pretty pictures on canvas. Awning companies sometimes paint or silk screen
signage on Sunbrella. Even back in the wooden boat
days it was pretty common practice to cover the wood
decking with painted canvas.
Test the paint you would would like to use on a small area or on a scrap piece first but you should be fine. Have heard of people using acrylic
house paint before.