I do not know of a canvas cover, but they do offer screening with various levels of sun blocking, from almost none to 25%, 50%, and 75%. If you are after canvas to block the rain, I think you will be out of luck as I do not believe the method used to secure the existing screening will hold up to the occasional high winds with canvas installed. It is possible that the entire structure might not be suitable for the wind load.
Hope this helps.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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