1. Round | 03/08/2019 | Ayr United | - | Greenock Morton FC | 4:2 | ||||
2. Round | 10/08/2019 | Greenock Morton FC | - | Alloa Athletic | 4:1 | ||||
3. Round | 23/08/2019 | Greenock Morton FC | - | Partick Thistle | 3:2 | ||||
6. Round | 21/09/2019 | Greenock Morton FC | - | Dundee FC | 1:0 | ||||
7. Round | 28/09/2019 | Dundee United | - | Greenock Morton FC | 6:0 | ||||
8. Round | 05/10/2019 | Greenock Morton FC | - | Dunfermline Athletic | 1:1 | ||||
9. Round | 19/10/2019 | Arbroath FC | - | Greenock Morton FC | 1:0 | ||||
20. Round | 04/01/2020 | Arbroath FC | - | Greenock Morton FC | 1:2 | ||||
21. Round | 11/01/2020 | Greenock Morton FC | - | Dunfermline Athletic | 3:2 | ||||
17. Round | 08/02/2020 | Greenock Morton FC | - | Queen Of The South | 2:2 | ||||
24. Round | 25/02/2020 | Ayr United | - | Greenock Morton FC | 1:2 | ||||
26. Round | 29/02/2020 | Queen Of The South | - | Greenock Morton FC | 0:4 | ||||
27. Round | 03/03/2020 | Inverness CT | - | Greenock Morton FC | 3:2 |