What can I do if non-custodial parent wants out of state visitation but won't provide his address?

Generally, your timesharing arrangement will be governed by the language of your court judgment or order and any written agreement made a part of it. Many court orders and judgments and most agreements require each parent to keep the other apprised of their residence address. It is rather unlikely that a court would make you send your kids or one of them to him for timesharing without knowing something as basic as his address so you know where they are. The fact that he moved out of state several years ago and you never addressed it in terms of formally modifying your existing court order or judgment and/or agreement suggests that you're reasonable, but you really should have the out-of-state timesharing formalized. It would be advisable for you to consult with an attorney to review your judgment/order and any agreements, and to discuss the specifics of your situation and your options.

You have a perfect right to know where your children are at all times. including the address. But before you refuse this, have a full discussion with a local attorney.