A right-handed batsman and a right-arm fast round-arm bowler, Conway played for Victoria in Australia.

He acted as the Australian agent for the English team that toured Australia in 1876–77, and towards the end of the tour he arranged for the leading players from New South Wales and Victoria to play a "Grand Combination Match" against the English team at the Melbourne Cricket Ground.

Despite the objections of the state cricket associations, Conway organised and managed the inaugural Australian tour of England in 1878.

[6] For many years, Conway worked as a journalist covering football, cricket, horse racing and coursing.

[7] Attendees at a small private funeral included Tom Horan and Frank Allan from the 1878 team.