Númenóreans are known to have leveled large forests in Eriador and in (the later) Gondor in their greed for shipbuilding-wood. Did they ever have trouble with the Ents?
This is never explicitly mentioned
There may be one reference, made it passing, that may refer to Numenoreans.
Indeed I have not seen them roused like this for many an age. We Ents do not like being roused; and we never are roused unless it is clear to us that our trees and our lives are in great danger. That has not happened in this Forest since the wars of Sauron and the Men of the Sea.
an earlier passage with similar wording "The war between Sauron and the Men of the Sea", however, has been speculated as in fact being the War of the Last Alliance, which involved Sauron and the Men of the Sea after they'd cut down all the trees and not while they were chopping them down. It is likely that this is the same for the original quote, as during the chopping of the trees by the Numenoreans, Sauron was under the pseudonym Annatar, and although it is possible that Treebeard has realised that Annatar was Sauron, it is unlikely.
So if there wasn't a clash between the Ents and the Numenoreans, why didn't the Ents protect their trees?
Well, the Ents were created (or the spirits were sent into trees) to protect against the fell things in Middle-earth (including Dwarves), those creatures that were not the Children of Illuvatar, that would not care for killing the trees.
It is also likely that the might of the Numenoreans drove the Ents back, as they didn't have great strength, although their strength in the Elder days was greater than in the end of the Third Age.
No idea, honestly
It would seem that the Númenóreans felled trees near Vinyalondë, the haven for the Númenóreans of the Second Age. For this reason they were in feud with the men living near the area, but there is no mention of feuds between the Ents.
From the letter of Gil-galad to then King of Númenór, Tar-Meneldur.
So the Lord Aldarion long has seen. At Vinylondë by the mouth of Gwathló he has long laboured to establish such haven, secure against sea and land; but his mighty works have been in vain. He has great knowledge in such matters, for he has learned much of Círdan, and he understands better than any the needs of your great ships. But he has never had men enough; whereas Círdan has no wrights or masons to spare.
Unfinished Tales of Númenór and Middle-earth: Part Two, II, Aldarion and Erendis
Here follows the part of their feuds with men in the area (in the previous chapter):
But for long the crews of the great Númenórean ships came unarmed among the men of Middle-earth; and though they had axes and bows aboard for the felling of timber and the hunting for food upon wild shores owned by no man, they did not bear these when they sought out the men of the lands. It was indeed their grievance, when the Shadow crept along the coasts and men whom they had befriended became afraid or hostile, that iron was used against them by those to whom they had revealed it.
Unfinished Tales of Númenór and Middle-earth: Part Two, I, A Description of Númenór
It may be that Treebeard was "prejudiced" against Saruman for felling trees, in his territory. While we have no idea if the Ents' territories included Vinyalondë, it would seem it would have been unlikely for them to attack the Númenóreans, given their "good" nature as descendants of the Edain.