1946-47
1st Round Dunfermline Ath. (h) 6-2 9,961
2nd Round East Stirlingshire (h) 5-1 5,405
3rd Round Queen's Park (h) 3-1 12,500
Quarter Final Motherwell (h) 0-2 14,500
1947-48
1st Round Kilmarnock (h) 2-0 12,000
2nd Round St Johnstone (h) 5-1 12,000
3rd Round Dumbarton (a) 1-0 8,000
Quarter Final Rangers (a) 0-1 90,000
1948-49
1st Round Falkirk (h) 2-1 15,355
2nd Round Cowdenbeath (a) 2-1 23,350
Quarter Final Hibernian (a) 2-0 24,946
Semi Final Rangers (Hampden) 0-3 104,958
1949-50
1st Round Fraserburgh (h) 4-0 6,343
2nd Round Falkirk (a) 3-2 13,000
Quarter Final Stenhousemuir (a) 3-0 12,500
Semi Final Partick Thistle (Ibrox) 2-1 42,000
Final Rangers (Hampden) 0-3 118,262
1950-51
1st Round Celtic (h) 2-2 16,000
Replay Celtic (a) 2-4 36,185
1951-52
1st Round Eyemouth United (a) 4-0 2,500
2nd Round Airdrieonians (a) 1-2 15,700
1952-53
1st Round Vale of Leithen (h) 7-1 5,338
2nd Round Airdrieonians (a) 0-3 14,500
1953-54
1st Round Queen of the South (h) 0-3 14,500
1954-55
5th Round Kilmarnock (h) 1-2 11,000
1955-56
5th Round Stenhousemuir (h) 1-3 6,000
1956-57
5th Round St Johnstone (h) 4-0
6th Round Kilmarnock (h) 0-0 8,716
Replay Kilmarnock (a) 0-2 18,000
1957-58
1st Round Hearts (h) 1-2 13,750
1958-59
1st Round Aberdeen (a) 1-2 13,800
1959-60
1st Round Partick Thistle (h) 0-2 3,475
Edited to add the attendances (My records are missing the St Johnstone one in 1956-57 unfortunately...)