Would a swamp cooler be a good idea for cooling in Southern California?

It is a good source if properly attended to and the room is the correct size. If the room is too small, there could be humidity problems, and if the cooler isn’t properly filled and emptied, there could also be a mold problem.

When it is not being used, is the room adequately ventilated? There are many factors that have to be evaluated. Read the owners manual, and look for reviews online for the unit you would like to use.

I have a portable unit in my garage, so we can use it on the hot days, for a playroom and workshop.

It should cause any problems, per-se, but my old house used to have a swamp cooler, which we replaced after out first summer there because it didn’t do very much to keep the temperature down. It depends where exactly you live, but I would suggest central air if you can get it.

Swamp coolers work best where the humidity is very low. My grandparents always had a swamp cooler in El Paso, where the humidity often hit single digits. It worked fairly well there and was inexpensive to run and maintain as compared to regular air conditioning. It also added some much needed humidity to room air. I understand that, in addition to places like El Paso, swamp coolers are common in cities like Denver, Salt Lake City, Albuquerque, Tucson, and Fresno where sufficient water is available.

In highly humid climates, swamp coolers have little thermal comfort benefit beyond the increased ventilation and air movement it provides, which you can manage to get with a simple ceiling fan.

How humid is the area you live in?

http://www.cityrating.com/cityhumidity.asp?City=Los+Angeles

Los Angeles Relative Humidity (Morning) 79%
Los Angeles Relative Humidity (Afternoon) 65%

http://www.cityrating.com/cityhumidity.asp?City=El+Paso

El Paso Relative Humidity (Morning) 56%
El Paso Relative Humidity (Afternoon) 28%

If you don’t want really cold air in your house it might work, but it won’t make things as cool as air conditioning would. You might start by putting in fans. If you can exist using just fans and no AC, then you might consider a swamp cooler.

Here in Bakersfield they are great up to about 95 degrees then they don’t do much. Some people make the mistake of trying to use them WITH an AC. That doesn’t work because the AC works by taking humidity out of the air and the evaporative cooler works by running the air through water and puts humidity in the air.

When I grew up in LA (NE SF Valley) we had a swamp-cooler in the house and it seemed to work pretty well. But it’s my impression that’s LA is more humid than it used to be.
Possibly a century of watered lawns has changed the climate a bit.
By the time I graduated from high school (a few decades ago) my parents had installed a regular AC system. That worked better, but I’m quite sure it cost at a lot more to run it.