Does it cost money in NJ to unblock someones private cell phone number call pressing *69?

I do not know the answer to your question about unblock, but I suggest you contact the phone company.

*69 does not unblock their number, it just calls them back. And yes, it costs money, although it’s probably changed since the last time I checked a decade ago. You can’t unblock someone’s blocked number unless you’re a government agency (or perhaps a rouge international spy…).

I suggest you look in the phone book under the “Products and Services” section.
In my area *77 is Anonymous Call Rejection. It is free.
If you are being harassed *64 is “Call Tracing”. Immediately after recievng the annoying call you hang up and wait for the dial tone. Then dial *64 and wait for the message that says if the call was traced successfully. You then call the phone company Annoyance Bureau at 777-xxxx. If it is a life-threatening call, you dial 911.
There is a fee for the trace.

In New Jersey, at least:

*69 calls back the last number you received a call from.
*67 blocks your phone number from showing up on a caller ID.

I’ve tried and tried to get a number unblocked, and there’s no way to do it.