It’s difficult to say a constant climb rate for a B737-400, but I give you some information so you can determine an average climb rate (approximately):
Airspeed schedule: 280kt/.74M
Engines: CFM56-3C1 (23.5k) Isa+10ºC
To FL310: BRW 68,000kg (19min.), 52,000kg (12min.), 44,000kg (10min.)
To FL350: BRW 68,000kg (26min.), 52,000kg (15min.), 44,000kg (12min.)
V-Speeds V1, VR, V2 (Flaps 5, Temp. 20ºC, MSL):
68,000kg - 154, 159, 166
52,000kg - 132, 135, 146
44,000kg - 118, 121, 135
Optimum Altitude (Feet, All Engines, LRC and M.74)
68,000kg – 29500
52,000kg – 35400
44,000kg – 37000