Ibn Ka'b bin Malik narrates from his father (Sayyiduna Ka'b bin Malik, may Allah be pleased with him) that a woman slaughtered a goat with a stone. The Prophet (peace and blessings be upon him) was told about it, and he (peace and blessings be upon him) saw no harm in it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الضحايا / 19156
Mu'adh bin Sa'd or Sa'd bin Mu'adh (may Allah be pleased with him) said that a slave girl of Ka'b bin Malik (may Allah be pleased with him) used to graze goats on Mount Sal'. One of the goats was about to die, so she slaughtered it with a stone. The Messenger of Allah (peace and blessings be upon him) was asked about it, and he (peace and blessings be upon him) said: "There is no harm in eating it."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الضحايا / 19157
Sayyiduna Jabir (may Allah be pleased with him) said that the Prophet (peace and blessings be upon him) "granted a concession regarding the slaughtered animal of a woman, and of a child or a boy, when they slaughter it saying the takbir."
This chain has weakness in it. Al-Waqidi corroborated it regarding the slaughter of a boy, and he too is da'if (weak).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الضحايا / 19158
Sayyiduna Jabir bin Abdullah (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) ordered that the animal slaughtered by a boy be eaten: "When he slaughters it saying the takbir, it should be eaten." (b) Mujahid (may Allah have mercy on him) said: There is no harm in eating the slaughtered animal of a child, of a woman, and of the People of the Book.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الضحايا / 19159