The reference I could find to the Aisha hadith was Sunan Ibn Majah, Book of Nikah, Hadith 1934
Muslim Vol 2, Book 005, Number 2286:
Abu Harb b. Abu al-Aswad reported on the authority of his father that Abu Musa al-Ash'ari sent for the reciters of Basra. They came to him and they were three hundred in number. They recited the Qur'an and he said: You are the best among the inhabitants of Basra, for you are the reciters among them. So continue to recite it. (But bear in mind) that your reciting for a long time may not harden your hearts as were hardened the hearts of those before you. We used to recite a surah which resembled in length and severity to (Surah) Bara'at. I have, however, forgotten it with the exception of this which I remember out of it:" If there were two valleys full of riches, for the son of Adam, he would long for a third valley, and nothing would fill the stomach of the son of Adam but dust." And we used so recite a slirah which resembled one of the surahs of Musabbihat, and I have forgotten it, but remember (this much) out of it:" Oh people who believe, why do you say that which you do not practise" (lxi 2.) and" that is recorded in your necks as a witness (against you) and you would be asked about it on the Day of Resurrection" (xvii. 13).
Bukhari Volume 4, Book 52, Number 299:
Narrated Anas:
The people of the tribes of Ril, Dhakwan, 'Usiya and Bani Lihyan came to the Prophet and claimed that they had embraced Islam, and they requested him to support them with some men to fight their own people. The Prophet supported them with seventy men from the Ansar whom we used to call Al-Qurra'(i.e. Scholars) who (out of piety) used to cut wood during the day and pray all the night. So, those people took the (seventy) men till they reached a place called Bi'r-Ma'ana where they betrayed and martyred them. So, the Prophet invoked evil on the tribe of Ril, Dhakwan and Bani Lihyan for one month in the prayer.
Narrated Qatada: Anas told us that they (i.e. Muslims) used to recite a Quranic Verse concerning those martyrs which was:-- "O Allah! Let our people be informed on our behalf that we have met our Lord Who has got pleased with us and made us pleased." Then the Verse was cancelled.
These 2 taken together is further evidence...
Muslim Book 017, Number 4194:
'Abdullah b. 'Abbas reported that 'Umar b. Khattab sat on the pulpit of Allah's Messenger (may peace be upon him) and said: Verily Allah sent Muhammad (may peace be upon him) with truth and He sent down the Book upon him, and the verse of stoning was included in what was sent down to him. We recited it, retained it in our memory and understood it. Allah's Messenger (may peace be upon him) awarded the punishment of stoning to death (to the married adulterer and adulteress) and, after him, we also awarded the punishment of stoning, I am afraid that with the lapse of time, the people (may forget it) and may say: We do not find the punishment of stoning in the Book of Allah, and thus go astray by abandoning this duty prescribed by Allah. Stoning is a duty laid down in Allah's Book for married men and women who commit adultery when proof is established, or it there is pregnancy, or a confession.
Bukhari Volume 8, Book 82, Number 816:
Narrated Ibn 'Abbas:
'Umar said, "I am afraid that after a long time has passed, people may say, "We do not find the Verses of the Rajam (stoning to death) in the Holy Book," and consequently they may go astray by leaving an obligation that Allah has revealed. Lo! I confirm that the penalty of Rajam be inflicted on him who commits illegal sexual intercourse, if he is already married and the crime is proved by witnesses or pregnancy or confession." Sufyan added, "I have memorized this narration in this way." 'Umar added, "Surely Allah's Apostle carried out the penalty of Rajam, and so did we after him."
But muslims will counter with
None of Our revelations do We abrogate or cause to be forgotten, but We substitute something better or similar: Knowest thou not that God hath power over all things? Surah 2.106
Topic: Evidence that the Quran has changed