I've been during just about every time of year.
January - After the 1st and not over MLK weekend. Crowds are low, but the weather can be iffy. Parks close earlier and a lot of refurbishment happens during this time.
February - 1st two weeks, pretty much the same as January. Once you get to the 2nd two weeks you're into school winter breaks and the crowd levels increase a lot. Still have the iffy weather issue. Our school break is the last week of February. We've been and worn short and t-shirts the entire week and we've been and never got out of jeans, sneakers, long sleeve t-shirts and fleece jackets.
March - Higher crowds due to spring breaks.
April - Higher crowds due to spring break. Weather tends to be really nice though. Last week of April isn't bad because most spring breaks are over by then (although if Easter is late in the year that can be a factor).
May - Probably one of my favorite times to go. Weather is great without being too hot and humid. I try to stick to the first part of the month as I've found the crowds are lower. Some schools get out by mid to the end of May so as you get toward the end of the month the crowds increase a bit.
June, July, August - Hot and humid. Crowd levels definitely increase over the summer. If you go then I would go toward the end of August, when most schools are back in session.
September - Low crowds, but still hot and humid.
October - Again, one of my favorite months. The time around the long weekend is more crowded. Weather is great!
November - There's a week in November when a school system is on break (Jersey Week), so its more crowded then. Also over Thanksgiving week. If you avoid those two weeks you should have lower crowds. Weather is still good.
December - First 2.5 weeks have lower crowds, but the weather can be iffy. Last time we went it was the first week of December. 1st half of the week the weather was great, and then a cold front came in. By around the 20th the Christmas crowds start to arrive and it will get much more crowded.
Have a great trip.