Maynooth claimed a 2-0 win over Leeds AFC in the first round and have been rewarded with a trip to Turner's Cross to face the Leesiders who are looking for three consecutive FAI Cup victories.
The only all-Premier Division tie saw St Patrick's Athletic travel to Derry City whilst Waterford head to United Park to face First Division Drogheda United, who knocked out Shamrock Rovers in the first round.
First Division leaders UCD travel to CIE Ranch whilst Finn Harps, who beat Bray Wanderers in the first round, travel to Oriel Park to face Dundalk.
Bohemians face another First Division test, after beating Wexford in the first round, as they travel to Eamonn Deacy Park to face Galway United.
Premier Division side Limerick have been handed a home tie against Cabinteely whilst Shelbourne travel to the City Calling Stadium to face First Division rivals Longford Town to complete the draw.
Irish Daily Mail FAI Cup Second Round Draw
CIE Ranch v UCD
Cork City v Maynooth University Town
Derry City v St Patrick's Athletic
Drogheda United v Waterford
Dundalk v Finn Harps
Galway United v Bohemians
Limerick v Cabinteely
Longford Town v Shelbourne
All ties will be played on the week ending Sunday, August 26, with dates and kick-off times to be confirmed in due course.