Carrick Rangers, Donegal Celtic, Institute and Ballymena United also made it through to the round three draw.
BBC: Holders Glentoran progress in Co-operative Cup tie
Two IFA Premiership football games - Glentoran v Dungannon Swifts and Donegal Celtic v Linfield - were postponed.
BBC: Translink coach on snowy road
Dungannon Swifts edged out Donegal Celtic 4-3 in a Suffolk Road basement clash.
BBC: Glentoran defeat Crusaders in title clash
The Glasgow side are set to play Donegal Celtic on that date instead.
BBC: The Oval
Coleraine and Donegal Celtic have been given permission to speak to Hamill.
BBC: Darren Boyce could make his Glens debut in the Irish Cup
The proposed match against Donegal Celtic is likely to be staged at Suffolk Road as Casement Park is unlikely to be available.
If Donegal Celtic win the Championship, Institute will be relegated but they will go into a two-legged play-off if current leaders DC finish second.
BBC: Institute 1-1 Coleraine
"Someone at Glasgow Celtic had made a prior commitment that they would play Donegal Celtic if they ever came to Belfast, " explained Mr Rodgers.
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