Check into Emerson Adult School in Westchester. It is an adult school through the LAUnified school district, but they offer GREAT parenting classes. I know the spring semester started at the beginning of February and they have just added another baby class, so there might still be openings. The parenting classes do have a lottery system for getting in in the fall, but you might want to check this one out. The school is on Emerson off of Manchester Blvd. ###-###-####, call the main office for more information.
Also, check out the South Bay Adult School. www.southbayadult.org for their spring registration. They also have their parenting classes which are excellent too.
Oh, you might also want to check out the el segundo rec and parks. I know they have some great classes, so there might be something to get you through to some other class that you really want.