A Normal/Ghost-type, if introduced in Generation 1, would have no weaknesses (It would be immune to Normal, Fighting, and Ghost ; resist Poison). A Psychic/Ghost-type, if introduced in Generation 1, would have no weaknesses (It would be immune to Normal, Fighting, and Ghost ; resists Poison and Psychic). You, also, mentioned Ghost/Dark-type before Generation 6 having no weaknesses (which would be immune to Normal, Fighting, and Psychic ; resist Poison).
There are literally the only type combos that would have no weaknesses without the help of an ability.
If you are curious as to which others would have no weaknesses due to abilities, I will list them below:
Electric w/Levitate
Water/Ground w/Sap Sipper
Poison/Dark w/Levitate
Bug/Steel w/Flash Fire