Battery Park/WTC Area with 38 children
There's a new pizza place (Caravelli's) in the World Financial Center food court right across from the Memorial that may be able to accomodate you, given its proximity to the outdoor seating in the North Cove Marina:
You might want to call ahead if you're doing a weekend day (not sure how geared up they are on Sundays)...
220 Vesey St, New York, NY 10282
Harry's Italian Pizza Bar is in the Financial District and it looks like it can handle 50 people in their private room.
FYI, the main large pizzas ($18) are grandma's style (they don't do slices), so I would allocate an average of 3-4 kids to a pie.
2 Gold St, New York, NY 10038