Xtreme scuba in ventura rent CCR's. They have several CCR's and evan some SCR's
Of course there not exactly in LA proper.
If you are willing to dive OC

and air

and Reefseekers Dive Shop in Beverly Hills has a boat going out they can fix you up with everything...including a buddy. Aside from the two salient points, there boats are well run and it would be a good time.
I'm not sure who rents CCR aside from SSA in Montclair. You should check with them as they could probably fix you up with one of their boats going out. They usually have a 6 pack going out every other week for training.
Stefan might know of other places that rent CCR's.
Jerry