The Ross Avenue motel catered to traveling African Americans up until the 1960s. Before that time, it was almost impossible for black travelers to stay in hotels in Dallas. Even famous African Americans avoided dealing with the situation by staying in local homes when booked to perform in Dallas.
The book I am taking this information from, Dallas Landmarks, does not indicate when the hotel was built, but the post card is probably from the 1940s. The hotel became nevermore in the 1960s because a) African Americans had more choices when it came to hotels and b) most people wanted to stay near the new highways while traveling.