Poyet joins Jose Mourinho, Manuel Pellegrini and Tony Pulis in being nominated for the January award.
Johnson is one of four nominees for the Player of the Month after scoring five Premier League goals for Sunderland including a hat-trick at Fulham and the winner against Stoke.
Yaya Toure, Santi Cazorla and Luis Suarez are also in contention for the monthly gong.
Both Suarez and Pellegrini are in contention for back-to-back awards after picking up the prizes for December.