My fellow posters...I've read through the postings and am surprised that the obvious solution was missed. Each and everyone of us should make a request for napkins, placemats & coasters along with our reservations. Like the high chair they may magically re-appear as an automatic amenity in the room.
Actually I was wondering why there was a pak-n-play in my studio last weekend.
I also agree with the person who advocated durable disposable coasters. High quality paper dinner napkins, durable paper placements and coasters may be the way to go. Restock if used during the course of the stay.
P.S. To be honest the only thing I would bother with, with any frequency, would be the coasters.