The bringing of Nimloth to Númenor is described in a very broad account of the early days of Númenor that covers events unfolding over hundreds of years within a handful of paragraphs. Thus it is hard to pin down the date of the tree's arrival with any degree of certainty, except to say that it was probably within the early centuries of Númenor's existence.
The late KingTar-Palantir made a prophesy that when Nimloth died, the Line of Kings would come to an end. If the survival of Nimloth was tied so directly to the line of the Kings of Númenor, this might rather tenuously suggest that it dated back to the time of Tar-Minyatur the first King, but this connection is circumstantial at best.
We can date the destruction of Nimloth a little more closely than its planting, though still not precisely. When Isildur stole one of its fruit, Ar-Pharazôn was persuaded by Sauron to destroy the tree. After this event we're told that '...the years passed, and the King felt the shadow of death approach, as his days lengthened' (Akallabêth) before he began his Great Armament in defiance of the Ban of the Valar. We can date this latter event as II 3310, so the burning of Nimloth must have been several decades previously, probably about II 3290, but perhaps even as early as c.II 3270.