Evil Children

[Lord of Angmar]

Evil is fissiparous. But itself barren. Melkor could not 'beget', or have any spouse (though he attempted to ravish Arien, this was to destroy and 'distain' her, not to beget fiery offspring).

Morgoth's Ring--Myths Transformed

This is a quote provided by Angry Hill Troll in the uhg- A terrible thought thread. I would assume that the same held true for Sauron. As for before their respective 'falls', I would think that yes, perhaps they could have had children, though not with other Ainur. Since Melian wedded Thingol and bore him a child, I would thing that Sauron could have begotten offspring with a Child of Iluvatar (the chances of Melkor doing so are probably less, since the difference between a Vala and a Child of Eru would be, in my opinion, too great).