BBC Scotland will broadcast live television coverage of the Dundee v Bonnyrigg Rose Athletic and Queen's Park v Queen of the South cup ties.
The Scottish Cup second round game at Hampden will take place on Friday 8 January, kicking off at 19:45 GMT.
The tie at Dundee's Dens Park is on 9 January, also at 19:45.
Queen's Park's 3-1 win over Dundonald Bluebell was broadcast live on the channel last month, with the Spiders needing extra time to get through.
Premiership sides enter at the third round.
Scottish Cup second round
Ties to be played at 15:00 on 9 January, except where stated
Queen's Park v Queen of the South (19:45, 8 January)
Airdrieonians v Edinburgh City
Alloa Athletic v Cove Rangers
Arbroath v Falkirk
Buckie Thistle v Inverness Caledonian Thistle
Camelon or Brora Rangers v Heart of Midlothian
Dumbarton v Huntly
East Fife v Tranent
Elgin City v Ayr United
Forfar Athletic v Linlithgow Rose
Formartine United v Annan Athletic
Fraserburgh v Banks O'Dee
Greenock Morton v Dunfermline Athletic
Keith v Clyde
Kelty Hearts v Stranraer
Nairn County v Montrose
Partick Thistle v Cowdenbeath
Peterhead v Stenhousemuir
Stirling Albion v Raith Rovers
Dundee v Bonnyrigg Rose Athletic (19:45)