Hunting birds during the sacred months is permissible, because what is forbidden during the sacred months is only fighting. But many scholars, or most of the scholars, say that the prohibition on fighting during the sacred months has been abrogated.
But if the birds are inside the boundary of the sanctuary, then it is not permissible to hunt them, because the Prophet (blessings and peace of Allah be upon him) said, when he conquered Makkah: “Its game is not to be disturbed.” If it is forbidden to disturb the game, then killing is even more forbidden. And Allah says (interpretation of the meaning):
“O you who believe! Kill not the game while you are in a state of Ihraam [for Hajj or ‘Umrah (pilgrimage)]”
“Lawful to you is (the pursuit of) water game and its use for food — for the benefit of yourselves and those who travel, but forbidden is (the pursuit of) land game as long as you are in a state of Ihraam (for Hajj or ‘Umrah)”
If a person is in ihraam or is within the boundaries of the sanctuary, then it is not permissible for him to hunt. End quote.
Majmoo’ Fataawa Ibn ‘Uthaymeen, 22/230, 231
For more information please see the answer to question number 97216