New York does not allow silent trusts, New Jersey allows them if the beneficiary is under 35 years old. There are states- Delaware for example- where they are allowed, so if you are interested in this type of trust, you can create one under the law of another state.
Basically, a silent trust is one where you don't tell the beneficiary that the trust exists. One of the big reason that people do this is to avoid "spoiling" their children.The thought is that if you tell the child that they have money coming, the child will not work.
I generally do not recommend them, if your beneficiary doesn't know about the trust then they won't be able to monitor the trustee to make sure the trust assets aren't misappropriated.
If you are concerned about leaving money to your child, there are better ways to go about transferring the assets than a silent trust. You can stagger payouts, or you can put conditions on distributions.