1 degree stepper motor
One way to increase the resolution so that you can make steps close to an exact one degree is to use a microstepping driver. 



That kind of driver works by PWM-modulating the current to the motor coils in a ratio that allows the rotor to stabilize in a position between the poles. You can't really increase the resolution by a huge factor, despite the driver stepping in (say) 128 or 256 microsteps but it might be good enough for you. 

If you had 8 microsteps on a 1.8 angular degree motor, then each step would represent 0.225 degrees, and every 40 microsteps (9°) you'd be back to an exact full step. 

You can make your own, or there are commercial suppliers such as Gecko.