If it's a Ph.D. program, you really will not have time to work. Psy.Ds will have a little more free time because of the lack of the research component..but still..very few people work outside their program. Many programs forbid it, or you have to get approval from your adviser/mentor before you can. Part of the reason why programs are support you with a modest stipend is so you can stay out of work and have full immersion and full attention to your studies. But, I do know some of the NYC schools don't have very good support for their students, so this is an understandable concern. I would consult with your program to see what their policies are. My adviser is the assistant PI for a grant at our med school, so, in addition to my stipend, I do get paid to SCIDs and testing for participant inclusion. But it only amounts to about $100/week. Certainly nothing I (we) could live on. Moreover, this is part of my lab technically, so I'm not sacrificing my research productivity. I am also pulling my dissertation data from these studies. This is why my adviser is cool with it.
If your program will allow you to work, you will not have much time to devote to it. If your working over 15 hours a week, you're probably going to have problems pulling your share of the weight in your lab and/or your class work will suffer. Maybe a job as a mental health tech at an inpatient psych unit? NYC has a butt load of hospitals and psych units. Maybe check the local hospitals for per diem research positions? I'd say use Craiglists for the mental health tech type jobs and just check the websites of the academic med centers/hospitals for research positions. The faculty in your program are a good source for networking for the research jobs. If you get their approval to work, I'm sure they have some connections that they can hook you up with.