A.Y.
Not sure where you are exactly in Parsippany. If you are close to Morris Plains, check out the Morris Plains Coop. I enrolled my 2 y/o dd there for september. Here is a link of their website.
http://morrisplainsco-op.org/
The deadline for new student enrollment was jan 31, so if there is no spot open, you have the waiting list option.
The nice thing too is you can co-op and the tuition is cheaper if you do, but if you are not able to, you just pay a little bit more. The difference is minimal.
I've also heard that many parents like Joyful Noise, also in Morris Plains.