It is practically impossible to get someone convicted for adultery in Islam for a variety of reasons; but there is no disagreement about stoning (rajm) as the punishment for adultery. The Prophet ﷺ upon him peace, pronounced and carried out rajm upon three married Muslims - one man and two women - and two Jews, a man and a woman.
Stoning for adultery is mass-transmitted from the Prophet ﷺ upon him peace, both as verbal injunction (Hadith "The child belongs to the household where he is born and the adulterer gets stones") and actual deed (stoning of Maa`iz ibn Maalik, Allah be well-pleased with him) cf. al-Kattani, Nazm al-Mutanathir (p. 105-106 ß181-182). Furthermore, there is complete consensus in the first three generations of Islam - both in law and in its application by the Four Caliphs - that the hadd of adultery for the married is stoning, cf. Ibn Qudama, al-Mughni (8:158); Ibn Hajar, Fath al-Bari (12:118). i.e. some say there are no stoning verses on the Qur'an, whilst as far as I know, unmarried individuals get lashes and banishment, whilst married people get lashes and stoning.
There are three types of abrogated Qur'anic verses:
(1) recitation-abrogated and ruling-abrogated
(2) recitation-established and ruling-abrogated
(3) recitation-abrogated and ruling-established
The verses that concern stoning as the punishment for a married person's adultery are of type (3) cf. al-Suyuti, al-Itqan fi `Ulum al-Qur'an (Type 47 of the Qur'anic Sciences, 2:718 of the Mustafa al-Bugha 1993 2nd edition, Dar Ibn Kathir).
[Note: in the case of "forcible adultery" (zina bil-jabr) i.e. rape - then the offender also faces death or (short of enough proof) long-term imprisonment regardless of marital status.]
See also Sa`d al-Mirsafi, Shubuhat Hawla Ahadith al-Rajm wa- Radduha (Beirut: Mu'assasat al-Rayyan, 1994) and Anwarullah, Criminal Law of Islam (Brunei: Ministry of Religious Affairs, 1995). islamqa.info (salafi site) gives several hadith showing how certain verses related to adultery in the Qur'an have been abrogated, according to the Sunnah. This is not entirely correct, as clarified already. (See separate post about the website quoted above.) And Allah knows best.
[1 Jun 2003]
"In any case, what Westerners call civilization, the others would call barbarity, because it is precisely lacking in the essential, that is to say, a principle of a higher order."
René Guénon, East And West, 1924
صلّى الله على سيّدنا محمّد و على آله و صحبه و سلّم
The blessings and peace of Allah on the Prophet, his Family, and his Companions, ( sallAllahu `aleihi wa sallam ) .