Praise be to Allah.
It is essential to stone the married adulterer until he dies, following the Sunnah of the Messenger (peace and blessings of Allaah be upon him), as it is proven that he said that, did it and enjoined it. The Messenger of Allaah (peace and blessings of Allaah be upon him) stoned Maa’iz, the Juhani woman, the Ghaamidi woman, and the two Jews. All of that is proven in saheeh ahaadeeth narrated from the Prophet (peace and blessings of Allaah be upon him). The scholars among the Sahaabah (may Allaah be pleased with them), the Taabi’een and those who came after them are also unanimously agreed on that. No one differed from them apart from those to whose views no attention is to be paid. Al-Bukhaari and Muslim narrated in their Saheehs from Ibn ‘Abbaas (may Allaah be pleased with him) that ‘Umar (may Allaah be pleased with him) said: “Allaah sent Muhammad (peace and blessings of Allaah be upon him) with the truth and revealed to him the Book, and one of the things that Allaah revealed was the verse of stoning. We have read it and understood it. The Messenger of Allaah (peace and blessings of Allaah be upon him) stoned (adulterers) and we stoned (them) after him, but I fear that there may come a time when some people say: ‘By Allaah, we do not find the verse of stoning in the Book of Allaah.’ So they will go astray by forsaking an obligation that Allaah has revealed. According to the Book of Allaah, stoning is deserved by the one who commits zina, if he is married, men and women alike, if proof is established or the woman becomes pregnant or they confess…”
Based on this, it is not permissible to replace stoning with killing by the sword or shooting, because stoning is a more severe punishment and a more effective deterrent to the sin of zina, which is the most grave sin after shirk and killing a soul whom Allaah has forbidden us to kill. The hadd punishment of stoning for a married person who commits zina is one of the matters that is determined by the Qur’aan and Sunnah and there is no room for ijtihaad or personal opinion. If killing by the sword or shooting were permissible in the case of the married adulterer then the Prophet (peace and blessings of Allaah be upon him) would have done that and would have explained it to his ummah, and his companions after him would have done that too.