Morrison has only recently returned from injury and played for 10 minutes, coming on as a late substitute, in the 1-1 draw with Everton on Wednesday night.
Cunningham has been an ever-present in Steve Bruce's team since joining in the close season from Wimbledon.
Full squad:
Goalkeepers: Shay Given (Newcastle United), Dean Kiely (Charlton Athletic), Nick Colgan (Hibernian) .
Defenders: Ian Harte (Leeds United), Gary Breen (West Ham United), Gary Kelly (Leeds United), Kenny Cunningham (Birmingham City), Steve Finnan (Fulham), John O'Shea (Manchester United), Phil Babb (Sunderland).
Midfielders: Jason McAteer (Sunderland), Matt Holland (Ipswich Town), Kevin Kilbane (Sunderland), Colin Healy (Glasgow Celtic), Mark Kinsella (Aston Villa), Lee Carsley (Everton), Rory Delap (Southampton), Stephen McPhail (Leeds United).
Forwards: Robbie Keane (Leeds United), Clinton Morrison (Birmingham City), Damien Duff (Blackburn Rovers), Gary Doherty (Tottenham Hotspur).