The time for throwing the pebbles begins at sunrise. However, the Sunnah is to throw the pebbles at the large Jamarah in daylight, some time after sunrise. Jabir (may Allah be pleased with him) said, “On the first part of the Day of Sacrifice (a short while after sunrise), the Messenger of Allah (peace and blessings of Allah be upon him) threw pebbles at the Jamarah while riding his camel.”[1] This Sunnah time continues until the sun passes the zenith. It is permissible to throw the pebbles from the time the sun passes the zenith until before true dawn on the 11th. The weak, those treated as being among the weak, and women are permitted to throw the pebbles during the night of the 10th, after Fajr and before sunrise. In short, the pebbles may be thrown from sunrise on the 10th of Dhu al-Hijjah until before true dawn on the 11th of Dhu al-Hijjah. During this period, go to throw the pebbles whenever you find a convenient opportunity.
[1]. Abu Dawud: 2/147.