What I could dig up on short notice...
Origin
In the manuscript of his notes for translators Tolkien stated that the Witch-king's name and background were not recorded, but that
he was probably of Númenórean descent.[1] It is unknown if his association with the realm of Angmar (or use of sorcery) can be traced to a time before he received one of the Rings of Power. In the Second Age, the Rings of Power were forged by the Elves of Eregion under Sauron's direction, and nine of these were given to men of the time, one of whom became the Witch-king. The rings gave them immense power, and they "became mighty in their day, kings, sorcerers, and warriors of old."[2] The rings also made them immortal, but eventually corrupted them, turning them into the ghastly, undead Nazgûl. The Witch-king became their leader.
The Lord of the Nazgûl served Sauron as his second in command for over 4000 years. He fought in the war against the Last Alliance of Elves and Men. When Sauron was defeated by the Alliance, the nine Nazgûl went "into the shadows".[3]
Campaign against Arnor
A millennium into the Third Age, the Witch-king reappeared in Angmar, a realm in the far North straddling the Misty Mountains. He quickly dominated Angmar, and turned to wage war against the three splinter kingdoms of Arnor (Arthedain, Rhudaur, and Cardolan); for Sauron, seeing that Gondor remained strong, sought to capitalise on the dissension among the northern kingdoms. It was during these northern wars, prosecuted against the Dúnedain for the next several hundred years, that the King of Angmar became known as the Witch-king. Rhudaur was soon compromised; power there was seized by evil Hillmen allied with Angmar. Argeleb I of Arthedain fortified the border against Rhudaur along the Weather Hills, but was killed in battle with Angmar and Rhudaur. The Witch-king then invaded Cardolan. King Arveleg I of Arthedain was killed defending Weathertop, but the palantír there was saved and moved to Fornost. The last Prince of Cardolan was killed, and most of the Dúnedain of Rhudaur were killed or driven out. Later the Great Plague destroyed many of the remaining Dúnedain of Cardolan, and evil spirits from Rhudaur and Angmar infested the burial mounds in the Barrow-downs.[4]
(All that was taken from the online Wiki
http://en.wikipedia.org/wiki/Witch-king_of_Angmar)
1300: Nazgûl reappear in Middle-earth, the kingdom of Angmar first appears at Arthedain's north-eastern border, built by the Witch-king,
later revealed as Lord of the Nazgûl. (But doesn't say exactly when).
2043: King Eärnil II of Gondor dies and his son, the Witch-king's old enemy Eärnur, inherits the throne. Upon his coronation, the Witch-king challenges him to combat, but King Eärnur refuses.
2050: The Witch-king again challenges King Eärnur, this time he accepts. Eärnur rides out of Minas Tirith to meet the Witch-king in Minas Morgul. He enters the city's gates and is never seen again, thus ending the reign of the Gondorian Kings and causing the beginning of the Ruling Stewards of Gondor, until the time of King Elessar.
3019
- March' 10: Frodo and Sam see the Morgul host led by the Witch-king leave Minas Morgul. An army from the Morannon takes Cair Andros and enters Anórien.
- March' 15: Witch-king breaks the gate of Minas Tirith in the early hours. Denethor burns himself on a pyre. Confrontation between Gandalf and the Witch-king at the gate; Horns of the Rohirrim are heard at a cockcrow. Battle of the Pelennor Fields: Théoden King of Rohan is killed by the Witch-king; Éomer succeeds him as the eighteenth king of Rohan. Éowyn and Merry kill the Witch-king. Aragorn, Rangers, the sons of Elrond and men from the southern fiefdoms of Gondor arrive in the black ships and turn the tide of battle. Sam and Frodo escape and journey along the Morgai. Battle under the trees in Mirkwood; second assault on Lórien.
(All this was taken from
http://en.wikipedia.org/wiki/Timeline_of_Arda#Second_Age)
Last bit...
..in
TA 1975, general Eärnur of Gondor landed at the harbours of the Grey Havens, leading an army of Gondor. His army was joined by the Elves of Lindon and the remnant of the northern Dúnedain and marched on the Witch-king.[1] At Fornost
They did not meet the Witch-king at Fornost, but on the plains west of it toward Lake Evendim, home of the ancient kings of Arnor, Annúminas. The battle would forever be known as the Battle of Fornost. Eärnur's Dúnedain army was later joined in the mists of battle by Glorfindel and his Elven army from Rivendell.
The Witch-king revealed himself and challenged Eärnur. As Eärnur attempted to attack, his horse was overwhelmed with fear of the Nazgûl lord and bucked. The Witch-king, taunting Eärnur, fled the battlefield. When Eärnur attempted to follow, Glorfindel stopped him with a warning that would become prophetic in the future:
"Do not pursue him! He will not return to these lands. Far off yet is his doom, and not by the hand of man shall he fall." ...sooo... after 1300 but no later than 1975?
How long would people think the "Witch-King" would live? What race did they assume he was? That might narrow the window down more since people would start to wonder how the Witch King lived so long maybe...?
The last comment... did the Elves know what the rings ended up doing to man and do they know who ended up with the ring? i.e. who wound up being the Witch King?