Good suggestions all. But if you choose to stick with your DC motor. Here's some ideas. I can picture them clearly enough, and I'm sure they could all be made to work with sufficient fiddling, but describing these mechanisms in words will be hard...
-Use a disc, (maybe a lid from something), as a reduction gear. Just press the motor shaft up against the edge. Friction drive. The centering does not need to be particularly precise as the motor can be loose mounted and pulled against the disc with an elastic band. You might need to add friction to the disc edge using glue or tape or a rubber band or something like that.
-Similar to above, but make it into a single stage pulley using an elastic band as a drive belt. You might need to 'machine' the edge of the lid for the belt to stay on.
-Coil an elastic band around the mirrorball spindle two or three loops, then extend both ends of the band in opposite directions, 90 degrees to the ball shaft. Pin one end to a fixed point, the other end is connected (glued?) to the end of the motor spindle. The motor spindle is in the same axis as the elastic band. Just like a rubber powered model airplane, the motor can twist the elastic band and this will turn the mirror ball as the band pulls tighter. The motor will need to turn for a fixed period, then relax for a while so that the elastic band can unwind and the ball should rotate in the other direction.
-Fix the motor to the mirroball spindle at 90 degrees (like a T where the top of the T is the motor axis and the vertical of the T is the mirrorball shaft). Wrap thread around the motor shaft, then pin each end. The motor will 'winch' itself along the thread. You'll have to reverse it before it goes more than 50 degrees or so. Maybe use an elastic band instead of thread for extra traction.
-Mount the motor on the same axis as the mirrorball spindle directly in line with it, with the shaft pointing down towards the mirror ball shaft, with a gap of (say) 2 inches. Connect the two spindles with an elastic band. The mirrorball shaft must pass through a wax bearing (a bit of candle is perfect). This will add resistance and damp the rotation. Spin the motor up at full power one way for a few seconds then reverse it for a few seconds etc. The mirrorball will turn slowly one way then the other.
-Mount the mirrorball directly onto the motor shaft. Drive it directly at 1000RPM, strobe the LED light so that the ball looks frozen. Tweak the speeds to make it seem to be rotating slowly.
Cheap and cheerful