Well for Nidoking I would suggest Offense, every time. Seeing as his speed is mediocre, you may as well bump his Special Attack/Physical Attack up with a Modest Nature or Adamant Nature respectively.
Nidoqueen is a different story. You could go for bulk offense and use a modest/adamant nature. But you could also use her great defensive stats and go for a Bold Nature to boost her Defense or a Calm Nature is you prefer Special Defense.
Nidoqueen is definitely the harder of the two Pokemon to pick a nature for, and I would say her role depends on the Pokemon on your team. If you need someone to take hits then go for one of the two defensively boosting natures. If you want a bulky offence or in-game Pokemon then Modest would work better.
But for Nidoking I would always go for Modest, as he is definitely an offensive based Pokemon.