Welcome to the boards!
It's an interesting question.
Looking at what we do know the Black Númenóreans were centered around the city of Umbar in the south (I note your name but as far as I'm aware Black Númenóreans are not specifically named among the inhabitants of Angmar)
Two Black Númenórean lords are named Herumor and Fuinur rose power amongst the Haradrim.
The power of the Black Númenóreans declines after the last alliance.
RangerofAngmar wrote:would we assume that the Black Númenóreans had a separate culture?
I think that it's reasonable to assume that over time the Black Númenóreans would have had developed a different culture from the Faithful simply as a result of the people and lands they were now rulers of. For example the Black Númenóreans are unable to keep pace with the naval might of Gondor and even lose the port of Umbar which surely would have seen a decline in the naval tradition of their people.
Looking at the limited evidence we have of the warfare and tactics used by their people (the Haradrim) we see them favouring cavalry and of course the Mûmakil, we see too the style of weapons change from the traditional Númenórean swords to scimitars.
Taking from our our limited sources they adopted other cultural traits such as clothing and so, though this change would have taken a long time I'm sure it occurred.
RangerofAngmar wrote: and even a different version of the Rangers of Arnor?
It may depend on where in the timeline you look.
In the earlier days before too much assimilation had taken place it is likely that the Black Númenóreans military structure would have been a bit more traditional had some sort of scouting group.
Based on later evidence it seems highly unlikely that the Haradrim had any sort of effective scouting or skirmishing troops. Faramir and the rangers of Ithilien are easily able to ambush the army en route to the Morannon. Likewise the Riders of Rohan are able to pass through the Rammas Echor without detection.
Even as a fighting force they don't seem to be equivalent the Rangers of the North. Theoden and his knights cast down the Southron chieftain despite their numbers whereas the smaller grey company are described as men without peer.
Looking at the Rangers of Arnor, they formed out of the survivors of Arthedain, before that they were more than likely a conventional fighting force. Their ranger skills and woodcraft would have been developed and honed in the subsequent years as they adapted to their new method of warfare.
The Rangers of Ithilien however form a more traditional commando unit, able to effectively operate behind enemy lines and yet also able to serve as front line troops, I think it likely that the pre fall Arthedain rangers were a similar force which makes it possible that a common unit existed amongst the Black Númenóreans before too much assimilation had occurred.
RangerofAngmar wrote:if so what would these rangers be like compared to their counterparts?
So while I don't think that the Black Númenóreans would have had a version of the Rangers we see in the Faithful I'm not one to stifle creative thought.
Looking at the location they settled and the people they came to rule I think that for warfare they most likely would have used mounted scouts or spies.
The corsairs of Umbar though are famous for their coastal slave raids so they very well could have used scouts to find where the softest targets were.
I could imagine them as a sort of Isma'ili assassin, certainly the description of the Haradrim clothing seems to match the mental image this brings up. Dressing in a lot of black and scarlet like the rest of the Southrons, perhaps even silk. If you move away from ridiculous Assassins creed cosplay you could manage something quite unique and well within the bounds of credibility.
I also think this would suit the culture of Harad, the people of that land are regarded as cruel and often quarreled among themselves which seems a perfect place for a group of skilled assassins.
Where the Northern Rangers are essentially a roaming band of knights errant and the Ithilien rangers are part of a larger Gondorian military, the Harad rangers would not need to be a defensive force.
Some food for thought, possibly not the answer you were looking for but I hope it helps.