How to serve custody papers to noncustodial parent who is unreachable?

Your lawyer would be best able to answer that question. However, if you are unable to locate the person you may need to hire an investigator and if that does not work you need to search on numerous platforms like Arny records, Phonebook etc. Do a due diligent search.

If that fails to locate the person ask the judge to serve the papers by publication. This is the last resort the judge would want to try and after that, you can be granted full custody if the other person is unreachable or not locatable.

It would be wise to work with an attorney if you can't locate the person. If you can locate them and they refuse to be served you can have them served by different ways.

Some servers serve by nailing at the door of the address s/he resides in for sure or leaving it with a family member with close contact or leaving at his or her desk at work or with the manager. Your attorney would know what to do.