A right-handed batsman (RHB) and a right-arm fast round-arm bowler (RF), Conway played for Victoria and made ten appearances in first-class matches. He played a single match for Otago in New Zealand.
Conway is best remembered for his work in organising the successful inaugural Australian tour of England in 1878. For many years, he worked as a journalist covering football, cricket, horse racing and coursing. He acted as agent for the three English cricket teams that visited Australia, in 1876-77, 1881-82 and 1884-85.