Stoning in Islam
The Qu'ran has no verses about stoning to death for any crime of any kind.
Some Islamic countries do have stoning to death, however below is what is actually specified in the Qu'ran:
100 Lashes
[24:2] (As for) the fornicatress and the fornicator [the term covers adultery], flog each of them, (giving) a hundred stripes, and let not pity for them detain you in the matter of obedience to Allah, if you believe in Allah and the last day, and let a party of believers witness their chastisement.
[24:3] The fornicator shall not marry any but a fornicatress or idolatress, and (as for) the fornicatress, none shall marry her but a fornicator or an idolater; and it is forbidden to the believers.
[24:4] And those who accuse free women then do not bring four witnesses, flog them, (giving) eighty stripes, and do not admit any evidence from them ever; and these it is that are the transgressors,
[24:5] Except those who repent after this and act aright, for surely Allah is Forgiving, Merciful.
[24:6] And (as for) those who accuse their wives and have no witnesses except themselves, the evidence of one of these (should be taken) four times, bearing Allah to witness that he is most surely of the truthful ones.
[24:7] And the fifth (time) that the curse of Allah be on him if he is one of the liars.
[24:8] And it shall avert the chastisement from her if she testify four times, bearing Allah to witness that he is most surely one of the liars;
[24:9] And the fifth (time) that the wrath of Allah be on her if he is one of the truthful.
Reconciliation
This passage looks to me as if it is about adultery, since it talks about a concealed child:
[2:228] And the divorced women should keep themselves in waiting for three courses; and it is not lawful for them that they should conceal what Allah has created in their wombs, if they believe in Allah and the last day; and their husbands have a better right to take them back in the meanwhile if they wish for reconciliation.
Confine to their Home
[4:15] And as for those who are guilty of an indecency from among your women, call to witnesses against them four (witnesses) from among you; then if they bear witness confine them to the houses until death takes them away or Allah opens some way for them.
[4:16] And as for the two who are guilty of indecency from among you, give them both a punishment; then if they repent and amend, turn aside from them; surely Allah is Oft-returning (to mercy), the Merciful.
Death Penalty
There is a concept in the Qu'ran that is spoken of the Jews, that might be said to comment against various of the current Islamic death penalties current:
[5:32] "We ordained for the Children of Israel that if anyone slew a person unless it be for murder or for spreading mischief in the land it would be as if he slew the whole people"