You don't mention the kind of plants you have in the pot, but my guess is that the culprit is too much water; not the algae.
To look for some suitable plants for this situation, let me introduce you to our Native Plant Database which allows you to search for 7,371 native plants by scientific or common name, or choose a particular family of plants. Scroll down to our Recommend Species Lists and click on View Recommend Species page. Click on Northern California on the map, and you will get a list of 286 commercially available native plant species suitable for planned landscapes in California. The Narrow Your Search box on the right side of the screen allows you to search for herbs that may be suited for your patio. For example, in the box, select: California under State, herb under General Appearance, and perennial under Duration. Check both Sun and Part shade under Light requirement and wet under Soil moisture. Click on the Narrow your Search button, and you will get a list of 12 native herbs for California that meet these criteria. Clicking on the scientific name of each plant will bring up its NPIN page which has a description of the plant along with growth characteristics and requirements, and in most cases, photos. As you look through the list, try to match up the plant with your growing conditions.
Here is a previous answer for a question from California that is similar. In your case, the problem seems to be too much water; in the previous question, it is too much shade. I think there is some information you can use here.