The Second Round tie has been scheduled to take place at Leamington's New Windmill Ground on Tuesday, 17th November.
Blues progressed to the Second Round of the competition with a 3-1 First Round away win against Solihull Moors at Damson Park on 13th October.
The Brakes made it to Round Two with a comprehensive 5-1 First Round home win against Bromsgrove Rovers on 22nd September.
Full Second Round draw:
Coventry Sphinx or Nuneaton Town v Banbury United
Leamington FC v Birmingham City
Cradley Town v Stourbridge
Alvechurch v Rugby Town
Sutton Coldfield Town v West Brom
Boldmere St Michaels v Burton Albion
Tipton Town v Wolves
Causeway United v Romulus