Stammers won the women's doubles title at the Wimbledon Championships in 1935 and 1936 with partner Freda James. She also won the women's doubles title at the 1935 French International Championships with partner Peggy Scriven. Her best performances in women's doubles at the U. S. National Championships were in 1936, 1937, and 1938 when she reached the semifinals and in 1939 when she reached the final. In the 1936 semifinal, she and partner Marble were defeated by Jacobs and Sarah Palfrey Fabyan 6–2, 21–19. In the 1939 final, she and partner James Hammersley lost to Marble and Palfrey Fabyan 6–1, 6–2.