FAI Ford Cup holders Sligo Rovers will travel to in-form Dundalk to begin their defence of the trophy.
The only other all-Premier Division tie sees Limerick host Bohemians.
Athlone and Longford will contest a midlands derby while St Patrick's Athletic face their amateur namesakes St Patrick’s CY in all-Dublin encounter.
FAI Ford Cup Round 2 draw:
Dundalk v Sligo Rovers
Belgrove/Home Farm v Finn Harps
Drogheda United v Cockhill Celtic
Limerick v Bohemians
Cobh Ramblers v Derry City
Athlone Town v Longford Town
Wexford Youths v Bray Wanderers,
Shelbourne v Waterford United
St Patrick’s CY v St Patrick’s Athletic
Mayfield United v Malahide United
Ballynanty Rovers v Phoenix
UCC v St Michael’s
UCD v Galway
Collinstown v Avondale United
Cork City v St Mochta’s
Sheriff YC v Shamrock Rovers.
Fixtures will be played the weekend ending Sunday 8 June.