My gut tells me this is not a good project for an event. I can't imagine there are any inks that would stick to oil cloth. Maybe Sharpie - but Sharpie isn't archival. Those little bottles of paint used for model building might work. One-Shot would probably work. But they both have a long dry time. And even then, you would not be sure if it would chip off after the paint cured - due to the flexibility of the cover.
Sometimes clients come up with really good ideas - but they don't know anything about the limitations of particular art supplies. Over the years, I have learned to avoid the search for unrealistic solutions. Clients hesitate to pay you for the time you spend experimenting and buying products to test. So if someone were to come to me with this idea, I would say - it will take $300 to experiment and look for something that works, and I seriously doubt I will find anything. They will whine and plead. Suggest they start thinking of alternatives. But there is no need to feel obligated to help them with their unrealistic expectation.
