League Cup holders Cliftonville will take on Dungannon Swifts at Stangmore Park in the third round next month.
The draw for the last-16 stage also sees Linfield at home to Ballinamallard while Crusaders host Institute.
Warrenpoint travel to play Portadown and Coleraine welcome H&W Welders, while Glentoran meet Carrick at the Oval and Ballymena travel to Limavady.
Ards face Glenavon or Annagh United, with the fixtures to be played on Wednesday, 14 October.
JBE League Cup third round
Coleraine v H&W Welders
Glenavon/Annagh Utd v Ards
Dungannon Swifts v Cliftonville
Portadown v Warrenpoint Town
Crusaders v Institute
Limavady Utd v Ballymena Utd
Glentoran v Carrick Rangers
Linfield v Ballinamallard Utd
To be played on Wednesday 14 October