The first thing is to figure out what not to do. You can't work in a field where people routinely hire full-time employees with ease. So you can't do Java work part-time, for example. (Well I mean you can, but it's like saying you can be elected to Congress. Let's do something easy.)
So, you have to start in some field where 9-5ers can't be easily found to fill the position. iOS/Android dev are like that. Maybe there are web specialities that are like that. If you have some deep expertise like machine learning or computer vision or graph algorithms, maybe those specialties are like that. But the operative criteria is to find some field that full-time employees are not easily had.
The next step is to filter by projects where time is not the biggest criteria. Because in spite of Fred Brooks and his MMM, ordinary people still believe that if you work more hours the project will get done faster, and will pressure you to become full-time. So you have to find people who are unconcerned about delivery dates, or rather, who have overriding concerns. Quality concerns. Cost concerns. If you find someone who has a fixed budget for his project, for example, if that person can get a better developer at 20 hours/week than he can at 40 hours that starts to look like an attractive value proposition. Because not only does he get a better developer, but with a lower burn rate it's easier for him to get deep visibility into where the money and time is actually going. Those benefits outweigh the benefits of completing the project faster, but only for projects that have these sorts of overriding concerns.
There's more you can do, but those two steps are probably all you need to start consistently landing part-time gigs.
It's worth pointing out as well, there are a variety of near-part-time deal structures you can negotiate (for example rotating 1 week on, 1 week off). These might be worth exploring depending on your specific motivations for seeking part-time work.