Homemade DC generator isn't outputting much voltage
It appears in your picture that you have two magnets that are not magnetically connected with a low reluctance material: -



Without the yoke (frame) the magnets in the picture above will not be very effective. The magnetizable material in the yoke ensures that field lines pass more effectively into the rotor.

I'm not ruling out other problems either because it's hard to tell from just a basic picture. Picture source: -


  The yoke is the outer cover of the machine supporting and protecting
  the internal parts. It is made of low reluctance ’ material like
  silicon steel or cast iron, Since, it has to carry the magnetic flux
  i.e., to provide the closed path for the flux produced through the
  poles.