The Ringwraiths were once Kings of Men and we know that mighty men like Denethor can use them and may even be able to briefly overcome Sauron like Aragorn did.
So could they use a palantir or does whatever they lost becoming wraiths prevent it?
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The Ring-wraiths were men, who's deaths had been prevented by the domination of Sauron. The greatest of the Ring-wraiths, the Witch-king, was a King of men and of great power. He, however, was not of the people's of Elros of Númenor. Albeit, his power was still far greater than that of the young Hobbit, Pippin, and just from his use of the stone it's likely they would have been able to use it, but not have had great success with it. It is also unlikely, since their wills were entirely dominated by Sauron, he would give them the chance to use it as he saw himself as a greater candidate for it's use.
It was the Númenoreans who had been gifted the palantíri by the Elves of Blessed Realm who had visited Númenor. Those who were most successful in using the stones where those who were "legitimate users", which were the "Heirs of Elendil" or those that "inherited authority":
In the case of Denethor, the Steward was strengthened, even against Sauron himself, by the fact that the Stones were far more amenable to legitimate users: most of all to true ‘Heirs of Elendil’ (as Aragorn), but also to one with inherited authority (as Denethor), as compared to Saruman, or Sauron.
Unfinished Tales - Part Four, Chapter III: The Palantíri
Denethor was able to deter the domination of Sauron because of his lineage, as well as his great will power and mental strength, unlike Saruman who quickly fell into deceit:
Saruman fell under the domination of Sauron and desired his victory, or no longer opposed it. Denethor remained steadfast in his rejection of Sauron, but was made to believe that his victory was inevitable, and so fell into despair. The reasons for this difference were no doubt that in the first place Denethor was a man of great strength of will, and maintained the integrity of his personality until the final blow of the (apparently) mortal wound of his only surviving son... And in the second place the Anor-stone was his by right, and nothing but expediency was against his use of it in his grave anxieties.
One could however risk contact with a stronger power purely by their strength of will, which Denethor had done, although his lineage would surely have played into this.
He must have guessed that the Ithil-stone was in evil hands, and risked contact with it, trusting his strength. His trust was not entirely unjustified.
It therefore seems likely that although the Ring-wraiths could most likely use the stone, they would've had their thought and deceit seen by either Denethor or Aragorn, since they were rightful users of the stones, and would have greater power by right.
Finally, a large extract on who could "rightfully" use the stones, the constant insistence that these are only the people who could "rightfully/lawfully" use it suggests that others could use them, but those that were granted it by right were more successful.
These Stones were an inalienable gift to Elendil and his heirs, to whom alone they belonged by right; but this does not mean that they could only be used rightfully by one of these ‘heirs’. They could be used lawfully by anyone authorized by either the ‘heir of Anárion’ or the ‘heir of Isildur’, that is, a lawful King of Gondor or Arnor. Actually they must normally have been used by such deputies. Each Stone had its own warden, one of whose duties was to ‘survey the Stone’ at regular intervals, or when commanded, or in times of need. Other persons also were appointed to visit the Stones, and ministers of the Crown concerned with ‘intelligence’ made regular and special inspections of them, reporting the information so gained to the King and Council, or to the King privately, as the matter demanded. In Gondor latterly, as the office of Steward rose in importance and became hereditary, providing as it were a permanent ‘under-study’ to the King, and an immediate viceroy at need, the command and use of the Stones seems mainly to have been in the hands of the Stewards, and the traditions concerning their nature and use to have been guarded and transmitted in their House. Since the Stewardship had become hereditary from 1998 onwards, 15 so the authority “or again to depute the use, of the Stones, was lawfully transmitted in their line, and belonged therefore fully to Denethor.
ibid, note #16
It appears that a strong will is necessary in order to get a palantír to work for you. The Nazgûl certainly have that.
Aragorn seems to suggest that his right of ownership helps him control it.
‘Nay, my friends, I am the lawful master of the Stone, and I had both the right and the strength to use it, or so I judged. The right cannot be doubted. The strength was enough – barely.’
The Lord of the Rings Book Five, Chapter 2: The Passing of the Grey Company
Page 780 (Single volume 50th Anniversary Edition)
However, I can find no indication that the Nazgûl's loss of what we would call a soul would prevent them from using a palantír.