Peter J. Conway (October 30, 1866 – January 13, 1903) was a right-handed pitcher in Major League Baseball for five seasons with the Buffalo Bisons (1885), Kansas City Cowboys (1886), Detroit Wolverines (1886–1888), and Pittsburgh Alleghenys (1889).

His older brother James Conway played Major League Baseball as a pitcher for the Brooklyn Atlantics and Philadelphia Athletics in 1884 and 1885.

"[9] One day after his Major League debut, Conway pitched his second complete game victory, this time against St. Louis.

[10] Two days later, The New York Times took note: "Conway, Buffalo's new pitcher, is handling the ball very cleverly.

The support given him, however, was of the worst possible character, and allowed the local men to tally unearned runs with apparent ease.

[8][14] After the 1885 season, the Buffalo franchise folded, and Conway signed with the Kansas City Cowboys of the National League.

Again, Conway played for a team that finished the year in seventh place, as the Cowboys compiled a 30–91 record.

[8] Conway was traded late in the 1886 season to the Detroit Wolverines, where he pitched 11 complete games in 1886 with a record of 6–5.

Conway traveled to New York in November 1888 to offer his services to other clubs at a meeting of the National League.

Conway indicated that he preferred to play for the Boston Beaneaters, where four of his Detroit teammates known as the "Big Four" (Dan Brouthers, Hardy Richardson, Jack Rowe, and Deacon White) had signed.

"[19] After talking with Fred Dunlap, a former teammate who had played for the Alleghenies in 1888, Conway ultimately agreed to sign a two-year contract for $3,500 per year.

"[22] The Alleghenies' suspension of Conway without pay following his injury sparked an early controversy over players' rights.

In August 1889, newspaper accounts noted: "Pete Conway will be backed by the brotherhood[23] in a suit against the Pittsburg club this fall.

"[26] By the beginning of August 1890, it was reported that "Conway has not drawn a dollar from the Brooklyn club" and that he was "at his home in Philadelphia.

H. T. Abbott, the student manager of the baseball team, attempted to hire Billy Sunday and Charlie Bennett, but both declined the offer.