Searches of Polk's City Directory turned up a Wiley's Restaurant which operated  for a four year period, 1924-1928  at  514 south 17th street. The same address is listed as the residence of Laura Wiley.  She is listed at that address before  and after the restaurant.  Her occupation is listed as a maid.

The paper search has gone no further than the city directory.

The postcard was published by S. H. Kress.  Perhaps this is the least known Birmingham business on a postcard.