I did a check on Paginas Amarillas and there seem to be tens of companies in the capital who do these, but none in Bavaro. I guess the companies in the capital will cover Bavaro, so it's probably a question of phoning round. If you do find a local company in Bavaro, it will probably be way more expensive because of the lack of competition.
Almacenes Unidos in Kennedy in the capital has got quite a good range of awning fabrics, so if you want to combine things like cushions or covers with your awning, one option is to buy your own fabric and get a company to make them up.
Another tip is to avoid the electric awnings and stick to the mechanical ones. The electric ones are crazy expensive here and will almost certainly break quickly, so go for something with a handle and a winder if you possibly can.