Cope joined Second Division Burslem Port Vale from Mount Pleasant in August 1904.[1] He played 25 games in 1904–05, scoring once in a 3–3 with Lincoln City at Sincil Bank.[1] The "Valeites" fared poorly, and finished third from bottom in the Football League, ahead of only Burton United and Doncaster Rovers.[1] Cope was a key part of the club's 1905–06 campaign, playing 38 games alongside defensive partner James Hamilton.[1] He played seventeen games in 1906–07, but left the Athletic Ground after the club resigned from the league.[1] In his three seasons at the club he made 80 appearances (73 in the league) and scored one league goal.[1]
He signed with nearby Stoke, also of the Second Division, and played 31 league and cup games in 1907–08. He was again without a club at the end of the season, as Stoke also resigned from the league due to financial difficulties.[3]
He left the Potteries and moved on to Oldham Athletic. The "Latics" finished sixth in 1908–09, and finished as runners-up in 1909–10 (one point behind champions Manchester City), thereby winning promotion to the First Division. Oldham pushed on in 1910–11, and posted a seventh-place finish. However, they struggled in 1911–12, surviving relegation by finishing just one point ahead of Preston North End. Athletic then finished ninth in 1912–13 and fourth in 1913–14. He had played 62 league games for the club, scoring one goal.
Cope signed with West Ham United as World War I began. The "Hammers" finished fourth in the Southern Football League in 1914–15, and Cope made 33 appearances. He was with West Ham for the duration of the war, and made 111 wartime appearances; the club won the London Combination in 1916–17 and were elected to the Football League in 1919. West Ham posted a seventh-place finish in 1919–20 and a fifth-place finish in 1920–21. Cope was appointed as club captain for the 1921–22 season, and led the "Hammers" to a fourth-place finish. He left the club at the end of the season; over the course of the three Football League campaigns he made 114 appearances.
Cope joined Third Division North club Wrexham for the 1922–23 season. Making thirteen appearances, he retired at the end of the campaign at the age of 38.