The dates of Malbeth's birth and death are unknown. He first enters history during the reign of King Araval, where we find him present at the birth of the King's grandson, Arvedui. This took place in the year III 1864, at least according to The Peoples of Middle-earth. Malbeth is a trusted advisor to the royal house at this point - it was he who suggested Arvedui's name to his father Araphant - so it seems likely he was born some decades earlier.
In The Return of the King III 5, Aragorn quotes Malbeth's prediction about his own future, and says that this was made '...in the days of Arvedui, last king at Fornost.' This seems to mean that Malbeth made the prediction during Arvedui's Kingship, which began in III 1964, exactly one hundred years after his birth. Whether Malbeth survived much beyond this point is unknown.