Options to cool attached sunroom
Keeping what is effectively a greenhouse cool in the summer is a heavy workload for any AC system. Your best bet is to prevent solar heat gain by blocking the light. Doing this with an opaque shade on the exterior will be the most effective option, though window tints or interior shades would also help.

Of course anything that reduces heating in the summer will also reduce it in winter. You may be able to exploit the fact that the sun is higher in the sky during summer than during winter, and create a shade that blocks more of the summer sun and less of the winter sun. This is often done architecturally by using long eaves over windows. But it's hard to retrofit a solution like that because it depends on the orientation of your sun room, the building around it, etc.

Because of all that, a retractable outside shade sounds like a great solution. If you're looking for a cheaper option than exterior motorized shades, you may consider a removable shade sail or an awning that you can wind away. The idea there is that you wouldn't be adjusting it every day, just seasonally and whenever there's a possibility of severe weather.