If you own, why not a self-supporting awning attached to the structure? Depending on the construction, etc, you might have to consider supporting on uprights attached to the ceiling joists, and cut some roof tiles for them to come through (easily weather-proofed with flashing, etc).
Something like these retractable awnings might do the trick. Not cheap, but easily done, and shouldn't even require a permit, depending on the planning rules in your city council. I know of models that have sun and wind detection - they come out automatically when sunny, and retract automatically when too windy.
If you rent, or cost/installation is an issue, then maybe find the largest cantilever umbrella you can?
Are you in Melbourne? A mate of mine has an automatic one with the sun and wind detection. Happy to find out who he went through, if you struggle to locate someone.