Points in the prayer at which du‘aa’ may be offered
Question

                What are the points in the prayer at which du‘aa’ may be offered?
Praise be to Allah.The points in the prayer at which du‘aa’ may be offered are of two types:
The first type:
Points for which there is evidence indicating that it is mustahabb and encouraged to offer du‘aa’, and it is mustahabb for the worshipper to offer du‘aa’ at length, as much as he wishes, asking Allah, may He be exalted, to meet his needs in general terms and aking Him for whatever he wants of good in this world and the hereafter.

When prostrating:

The evidence for this is the words of the Prophet (blessings and peace of Allah be upon him): “The closest that a person is to his Lord is when he is prostrating, so say a great deal of du‘aa’” Narrated by Muslim (482).

After the final tashahhud and before saying the sal aam: 

The evidence for this is the hadith of Ibn Mas‘ood (may Allah be pleased with him), that the Prophet (blessings and peace of Allah be upon him) taught them the tashahhud then said at the end: “Then let him choose whatever supplications he wishes.” Narrated by al-Bukhaari (5876) and Muslim (402).

In qunoot of Witr:

The evidence for this is the report narrated by Abu Daawood (1425) from al-Hasan ibn ‘Ali (may Allah be pleased with him), who said: The Messenger of Allah (blessings and peace of Allah be upon him) taught me some words which I say in Qunoot of Witr: “Allaahumma ihdini feeman hadayta wa ‘aafini feeman ‘aafayta wa tawallani feeman tawallayta wa baarik li feema a’tayta, wa qini sharra ma qadayta, fa innaka taqdi wa la yuqda ‘alayk, wa innahu laa yadhillu man waalayta wa laa ya‘izzu man ‘aadayta, tabaarakta Rabbana wa ta’aalayta (O Allah, guide me among those whom You have guided, pardon me among those whom You have pardoned, turn to me in friendship among those on whom You have turned in friendship, and bless me in what You have bestowed, and save me from the evil of what You have decreed. For verily You decree and none can influence You; and he is not humiliated whom You have befriended, nor is he honoured who is Your enemy. Blessed are You, O Lord, and Exalted).”
The second type:
Points at which it is narrated, in the description of the prayer of the Prophet (blessings and peace of Allah be upon him), that he offered du‘aa’, but without doing so at length, singling out these particular points or urging worshippers to ask for their needs in general terms; rather he offered du‘aa’ in brief and concise terms, with a specific wording. Therefore offering du‘aa’ at these points is more akin to dhikr that is said in specific words than to du‘aa’ in general terms.

Du‘aa’ al-istiftaah (opening supplication):

After the opening takbeer (takbeerat al-ihraam) and before starting to recite al-Faatihah.

When bowing:

The Messenger (blessings and peace of Allah be upon him) used to say: “Subhaanaka Allahumma Rabbana wa bihamdika, Allahumm aghfir li (Glory and praise be to You, O Allah our Lord. O Allah, forgive me).” Narrated by al-Bukhaari (761) and Muslim (484) from the hadith of ‘Aa’ishah.
In his Saheeh, Imam al-Bukhaari (may Allah have mercy on him) included this hadith under the chapter heading, “Supplication (du‘aa’) whilst bowing.”

After rising from bowing:

The evidence for this is the hadith of ‘Abdullah ibn Abi Awfa, according to which the Prophet (blessings and peace of Allah be upon him) used to say:
“Allaahumma laka al-hamd mil’ al-samawaati wa mil’ al-ard wa mil’a ma shi’ta min shay’in ba‘d. Allahumma tahhirni bi’ththalji wa’l-baradi wa’l-maa’ il-baarid. Allahumma tahhirni min adh-dhunoobi wa’l-khataayaa kama yunaqqa ath-thawb al-abyad min wal-wasakh.
(O Allah, to You be praise filling the heavens, filling the earth, and filling whatever else You will besides that. O Allah, cleanse me with snow and hail and cold water. O Allah, cleanse me of sins and errors as a white garment is cleansed of dirt).”
Narrated by Muslim (476).

Between the two prostrations:

The Prophet (blessings and peace of Allah be upon him) used to say between the two prostrations: “Allaahumma ighfir li warhamni wajburni wahdini warzuqni (O Allaah, forgive me, have mercy on me, console me, guide me, and grant me provision).” Narrated by at-Tirmidhi (284)’ classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
Imam an-Nawawi (may Allah have mercy on him) said:
The author of at-Tatimmah said: Du‘aa’ at this pointdoes not have to be in these specific words; rather reciting any du‘aa’ will fulfill the Sunnah, but what is mentioned in the hadith is better.
End quote from al-Majmoo‘ (3/437).
There are also reports which mention offering du‘aa’ whilst reciting Qur’an when standing in the prayer, either in naafil (supererogatory) prayers only, based on what is mentioned in the text, or also in obligatory prayers, by analogy with what is mentioned regarding naafil prayers, according to some scholars.
The evidence for that is the hadith of Hudhayfah (may Allah be pleased with him), according to which he prayed with the Prophet (blessings and peace of Allah be upon him). He said: He did not come to any verse that mentioned mercy but he paused and asked for mercy, and he did not come to any verse that mentioned punishment, but he paused and sought refuge with Allah from it.
Narrated by Abu Daawood (871); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
There are also reports which speak of offering supplication in qunoot an-nawaazil (qunoot at times of calamity), but the wording that is mentioned is mainly wording that is appropriate to the calamity in question, but if someone mentions different wording concerning other issues, then we hope that there is nothing wrong with that.
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
To sum up what has been proven from the Prophet (blessings and peace of Allah be upon him) about the points in the prayer at which he used to offer du‘aa’, there are six points, to which two more may be added:

Following the opening takbeer (takbeerat al-ihram):

This is mentioned in the hadith of Abu Hurayrah in as-Saheehayn: “Allaahumma baa’id bayni wa bayna khataayaaya kama baa’adta bayna al-mashriqi wa’l-maghrib. Allaahumma naqqini min khataayaaya kama yunaqqa al-thawb al-abyad min al-danas. Allaahumma ighsilni min khataayaaya bi’l-thalji wa’l-maa’i wa’l-barad    (O Allaah, put a great distance between me and my sins, as great as the distance You have made between the East and the West. O Allaah, cleanse me of sin as a white garment is cleansed from filth. O Allaah, wash away my sins with snow and water and hail).”

When standing up (after bowing):

This is mentioned in the hadith of Ibn Abi Awfa, which is narrated by Muslim, according to which he used to say after “…min shay’in ba‘d (besides that)”: “Allahumma tahhirni bi’ththalji wa’l-baradi wa’l-maa’ il-baarid. (O Allah, cleanse me with snow and hail and cold water).”

When bowing

This is mentioned in the hadith of ‘Aa’ishah: He often used to say when bowing and prostrating: “Subhaanaka Allahumma Rabbana wa bihamdika, Allahumm aghfir li (Glory and praise be to You, O Allah our Lord. O Allah, forgive me).” Narrated by al-Bukhaari and Muslim.

When prostrating:

This is the point at which he most often offered du‘aa’ and instructed others to do likewise.

Between the two prostrations:

“Allahumm aghfir li (O Allah, forgive me).”

In the tashahhud:

The Prophet (blessings and peace of Allah be upon him) also used to offer du‘aa’ in Qunoot, and when reciting Qur’an: when he came to a verse that mentioned mercy, he would ask for it, and when he came to a verse that mentioned punishment, he would seek refuge with Allah from it.
End quote from Fath al-Baari (11/132).
The most emphasized points in the prayer at which du‘aa’ may be offered are two, namely prostration and after the final tashahhud.
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
The points in the prayer at which du‘aa’ may be offered are prostration and the tashahhud.
End quote from Fath al-Baari (11/186; see also 2/318).
Shaykh Ibn Baaz (may Allah have mercy on him) said:
The point in the prayer at which du‘aa’ may be offered is prostration, and at the end of ‘at-tahiyyat’ (i.e., the tashahhud), before saying the salaam.
End quote from Majmoo‘ Fataawa Ibn Baaz (8/310).
And Allah knows best.