It's now 95 years in the US for material published 1923-1963, assuming the work was registered and renewed. Rodgers' publisher was Peer International, which has been diligent in protecting its copyrights. So the earliest anything will go PD under current law is late 2022 (1927+95; Rodgers' first recordings were made 8/4/1927); the last copyrights should expire in 2028 (1933+95; last session 5/24/1933).

However, a change in the laws between now and 2022, allowing even longer copyright protection, is pretty much guaranteed.