The best time to throw the pebbles is forenoon on the 10th of Zhul-Hijjah, because the Prophet (peace be upon him) threw the pebbles before noon on that day.
Ibn ‘Abbas said that the Prophet (peace be upon him) permitted the old and weak people of his family to throw first. Then he said, “Do not throw pebbles at the first Jamarah Al-Aqabah before the sunrise.” This was reported by Tirmizhi, who considers it a sound hadith. Deferring the throwing to the end of the day is, however, permissible.
Ibn Abdul Barr said: “There is consensus among the scholars that if a pilgrim throws pebbles on the 10th of Zhul-Hijjah before the sunset, he will be considered as having thrown in time, although doing so is not desirable.”
Ibn ‘Abbas reported that on the Day of Sacrifice the Prophet (peace be upon him) was told by a man at Mina that he had thrown his pebbles after sunset, whereupon he said to the man, “There is no harm.” This was reported by Bukhari.