Cup holders Crosshaven were knocked out in the first round leaving former winners Tullamore and last season's finalists Monivea as potential favourites.
Tullamore have been drawn away to Academy, who knocked out Richmond in the first round. Monivea have been given a home tie against Coolmine, who were hugely impressive in beating Tralee in the opening round.
Coleraine and Tuam will contest their first round tie on November 5 with the winners at home to Dundalk three weeks later.
All second round games will be played on November 26, with the semi-finals down for decision on February 4 and the final set for February 18.
ULSTER BANK ALL-IRELAND JUNIOR CUP SECOND ROUND:
1. Westport v Cooke
3. Monivea v Coolmine
4. Academy v Tullamore
List Of Previous All-Ireland Junior Cup Champions -
2011 - Crosshaven
2010 - City of Derry
2009 - Tullamore
2008 - Navan
2007 - Seapoint
2006 - Rainey Old Boys