Richard Butler Conway (April 25, 1866 – September 9, 1926) was a pitcher/right fielder who played from 1886 through 1888 in Major League Baseball.

His most productive season came in 1887, when he collected career-numbers in wins (9), starts (26), and innings pitched (222+1⁄3).

In a three-season career, Conway posted a 15–24 record with a 4.78 earned run average in 41 appearances, including 41 starts and 39 complete games, giving up 187 earned runs on 404 hits and 137 walks while striking out 121 in 352.0 innings of work.

He also played 18 games as an outfielder, compiling a career .230 batting average (47-for-204) with 27 runs and 14 RBI.

While at Boston in 1888, he also played briefly for the Hyannis town team in what is now the Cape Cod Baseball League.