Last season's CIS Cup runners-up Dundee United will take on Scottish Third Division side Cowdenbeath.
Last season's runners-up take on Cowdenbeath
Last season's CIS Cup runners-up Dundee United have been drawn against Cowdenbeath in the second round of the competition.
The Terrors, who lost to Rangers in March's final, will face the Scottish Third Division side at Central Park.
St Mirren also take on opposition from Scotland's fourth tier in the shape of Dumbarton, while SPL new boys Hamilton host Scottish First Division outfit Clyde.
Co-operative Insurance Cup second round draw:
St Mirren v Dumbarton
Livingston v St Johnstone
Dundee v Partick
Ayr v Aberdeen
Hibernian v Morton
Arbroath v Inverness
Hamilton v Clyde
Cowdenbeath v Dundee United
Hearts v Airdrie
Raith v Falkirk
Dunfermline v Alloa
Brechin v Kilmarnock
Ties to be played on Tuesday 26th August or Wednesday 27th August.