Which of these two magic skills should I pick along with illusion for my stealthy mage/nightblade character?

I would personally chose Alteration.

For stealth, alteration, no doubt.

Detect life and detect dead are indespensible.

Conjuration is really for a pure mage player along with destruction. All your conjurations automatically attack hostile enemies when they're nearby and casting will have enemies privy to your location.

My whiners answer would be not to take Illusion or Conjuration at all because it's going to make your game too easy.

My everything is fine answer would be to take Alteration if you're not going to use armour. Paralyze will help you get out of a couple tricky situations. The perks are also pretty decent. Transmute is also good if you want to make some quick coins or raise smithing/enchanting.

Thank you everyone, I think I'll go with alteration then.

I would use alteration but I didn't take any of the perks since there are only a few spells in it that I find useful and none of them need to be sustained long... Conjuration is pretty well useless for a stealthy character aside from using bound bow or soul trap but neither are any sort of requirement...