does a chicken coop/run need direct sun light

I am going to built a new coop this summer for my 5 girls and have 2 options on my property. One side is sunny and I would have to built a new coop/run from scratch, the other side has a 10X10 roofed structure and an additional 10x10 area under an evergreen tree. It only gets minimal direct sunlight under the structure and non under the tree. I would prefer using the existing structure because I can't garden there and the sunny side is ideal for gardening. I will take a picture of the structure and possible run area and would appreciate any input if that would be an option.
BTW. I live in the SF Bay Area and plan an very open coop. I think I only use hardware cloth to enclose the structure/ run and have the roost closed from 3 sides with the bottom being open and the non wind side open. That would be the plan even with the sunny side location.

 

Here are the pictures

 

No chance to remove the tree and it would not matter since my neighbor has evergreen trees on his side too. I could bumb it out but even than it would only get an hour or so late afternoon Sun.

 

Pirategirl. I know that I have to protect the top around the run. There are actually raccoons living/sleeping most nights in the neighbors evergreen tuja tree hedge. The other/old run is electrified and the coop is totally safe but one reason I am rebuilding is that I want the run area also predator proof since I am scared that one day I forget to lock them in or the electric fence fails.