From what I have learned, the most successful neutron guns have been produced at home using radium paint (found in glow in the dark clocks at antique stores) placed inside of a thick lead box. A hole can be made in one side where the alpha particles will escape and will meet with a piece of beryllium foil. I caution you though, don't play around with radioactive materials and radiation (especially neutron radiation) unless you know how to use it and what safety precautions to take.
Also, as a quick question to all on this forum, is there any research available online concerning what metals would be best for converting alpha particles to neutrons? This would be some research comparing different metals to see which would be most efficient for generating the neutrons.
