Care.com

My mom found good CNA options for my dad using Care.com.  Most of the people there are independent so it requires that you interview and vet them, but she has been quite happy with those she has found.

Hi! We moved to the Bay Area from North Carolina right before my son was due, didn't know a soul and had no family in the area, so your post resonates with me. We had luck with Swiss cheese for date nights--they vet their sitters and we felt comfortable with all of them. You can also chat with them before you book so you have control of your choices. We also used care.com to find our permanent part time nanny and she was great.  Another idea if you're not in a hurry--hang around the toddler parks in Oakland and Berkeley and chat with other moms and nannies. If you mention you are trying to find someone you might make a connection.  

I started out looking for part-time help for my folks and found my wonderful caregivers on Care.com. You set the parameters for what you need and look for someone who fits your needs.  There are lots of people out there, so be sure you interview them, run the background & DMV checks (provided through the site), get references and find the right fit (can you tell I work in HR?).  Good luck!