Groundcover for erosion control
It looks like you have a lot of weeds in your dry stream bed and you'll want to get rid of those before planting.
Kinnickinck (Arctostaphylos uva ursi) and Ceanothus ground cover are two evergreen ground cover choices that will do great in a sunny area. Buy flats and plant them 18-24 inches apart and they will fill in quickly. The first is native to Oregon and the second is native to California. You could also plant both kinds in clusters.
Juniper ground cover is another choice that will do well in that location.