I don't know if they make sleeves for playbills. Back in the day, I would buy plastic sleeves for my import 12 inch records to fit over the record. Obviously, one playbill would be to small for one sleeve, but two playbills would fit fine. I think they still sell them. If they do, maybe inquire about plastic sleeves for old 45's. They would fit one playbill really good. Out there thought, but at least a thought.
If they are the same size as modern Playbills you can get sleeves on the Playbill store. They are meant to be used in the binders they also sell, so they'll have the three hole punched strip along the side, but they'll still offer protection whether you use the binder or just put them in a box.
If they are the same size, I got Samsill mini clear 5.5x8.5 heavyweigt sheet protectors. Just made binders for the past 10 years of Playbills I have. I used Avery mini binders. Got them all on Amazon. It was much cheaper than Playbill. The binders come with a label you can slide into a clear holder on the spine.