Powerade Towns’ Cup holders, Clogher Valley, will start the defence of the trophy with a home game against Coleraine.
The draw for the second round was made at the Ulster Branch competitions committee in Belfast last night.
Kukri Section Two side, Coleriane, caused an upset in the first round when they defeated Section One side, Ballymoney in the first round.
Clogher at The Cran will pose a sterner threat.
Portadown entertain Drmore at Chambers Park in the only all Kukri One clash and another of the fancied sides, Bangor will travel to play Armagh II.
Tie of the round is likely to be the derby game between Banbridge II and Ballynahinch II at Rifle Park.
Enniskillen, who enjoyed a semi-final run in the Junior Cup will be favourites to win at home against Ards II.
Carrick, extra-time winners against Ballyclare in the first round have a home draw when they face City of Derry II.
Larne will take on Ballymena II and Donaghadee entertain Holywood in the remaining fixtures.
Ties to be played on or before Saturday, January 24