Separately excited DC generator as a constant current source
Back Torque in a DC generator is proportional to armature current x armature flux.
So if as you say you keep the flux constant Back Torque is proportional to armature current. So constant torque constant current.
The problem is that in order to maintain constant torque you are going to have to alter the speed of the generator. This involves a system which can measure the torque or current and an appropriate governor on the prime mover. The practicality of this depends on a number of factors the main one being the required output power range and the torque curve of the prime mover.
Most generators are designed to operate at one speed which corresponds with the optimum operating point of the prime mover.
As has been said in the comments it is probably simpler to implement some sort of electronic constant current source.