Creating custom weapons has two steps. (This isn't intuitive - you will need to do BOTH steps.)
First, go to the custom weapons profiles section, and Add a new profile with the + button, filling out the fields for the weapon stats.
Second, go to the custom equipment section at the top of the "custom" page, and add a new item with the + button there, and set the price and rarity, and whose equipment lists it will appear in, and choose the profile that you created earlier from the drop down menu (the weapon type will have to match in both the custom profile and the custom equipment item).
THEN it should appear in the appropriate section of the equipment options for the appropriate gang.