Newer
tops are acrylic or polyester, some older or replacement
tops are vinyl coated cotton, only really old
tops are cotton.
Anything that is appropriate for outdoor fabrics should be OK, as the newer
tops have to be made to withstand a car wash. Apply, scrub LIGHTLY with a soft brush, rinse. Apply appropriate outdoor fluorochemical treatment. Find out what the maker recommends before you take the job! (For example, Sunbrella will require you to use 303, at a significant extra cost over what you're used to paying for protectant.)
If you use the wrong stuff, you can damage the color. If you use water over 80 degrees, you'll shrink the top. If you use a high-pressure washer, you'll risk damage. It might have leaked before you started, but any convertible top or boat cover you do will leave you with the liability that it will leak when you're done. Even light degrees of moss can damage the top to the point that it will leak when clean. Boat
tops may still be sewn with cotton thread, which can come to pieces as you clean. Check out replacement costs before you decide you can make a quick buck doing this.
Winsol makes specific chemicals for outdoor fabrics, or see what's available at the local boat shops.