If what you need is reliable part time work, then a large company is the way to go. Small companies and freelancing may work out, but they are most likely to be less reliable.
The core of the problem is that it goes against the grain of common employment wisdom. IE. the more hours in the office, the better the employee.
This problem has been studied quite a bit and the general research shows that most employees who are able to work part time must start off a new job in a full time position, then request the change once they prove themselves. This is far from ideal; however, @Mark's suggestion that you look for a full time job where you can work from home is a good one and could provide a nice transitional period to prove your abilities before you request reduced hours.
Alternatively, some large companies (notably HP) have made large strives in making work places that accommodate working parents (specifically women, though the policies started when a senior male executive became a single parent and realized how hard it is) by providing a number of flexible work arrangements. Targeting companies with these policies could be a great place to start.
Another growing trend is job sharing where you work a single job in conjunction with another employee. Again, you'll mostly see this arrangement at progressive and large companies, but it lets you work part time without placing the burden on co-workers. In this team arrangement, you usually pitch the idea with a "partner" in mind and you both would have to work seamlessly ie share email and have someone covering every hour of the work day.
I was hoping to see another answer that would provide more direct advice, but this really is an ongoing problem. Many women and men find themselves in positions where a traditional 9-5 is impossible and the working world hasn't caught up. Keep an open mind and look into all the flexible work arrangements, not just part-time.