Oh there are places to get modern, period correct tires. For example Summit Racing and JEGS both sell Goodyear Polyglas replicas. They’re about 2x the cost of a standard tire though. I’m not sure about these skinnies, my knowledge runs out around 1955-1960. Anything before that and I couldn’t say.
These pre-war cars used bias ply tires that are somewhat harder to find but not impossible. Here is one I found that would fit this exact car, a 1930s Packard 1104 series:
That said, there are many modern conversations using "bias look radial" that are high profile radial tires that should fit the original rims, look mostly authentic yet give much better grip and traction.