Some Du’a’s to be recited during prayer
Question

Are there any particular Du’a’s to be recited during the prayer?.
Praise be to Allah.Perhaps the questioner is referring to du’a’s during prayer. 
It should be noted that the best of guidance is the guidance of Muhammad (peace and blessings of Allah be upon him) and the best of du’a’s are those which are in accordance with the Sunnah of the Prophet (peace and blessings of Allah be upon him). The Muslim should strive to follow the Prophet’s wording without adding, taking away or changing anything. 
It was narrated that al-Bara’ ibn ‘Aazib said: The Prophet (peace and blessings of Allah be upon him) said: “When you go to your bed, do wudoo’ as for prayer, then lie down on your right side and say: 
Allahumma aslamtu wajhi ilayka wa fawwadtu amri ilayka wa alja’tu zahri ilayka raghbatan wa rahbatan ilayka, la malja’a wa laa manjaa minka illa ilayka. Allahumma aamantu bi kitaabika alladhi anzalta wa nabiyyika alladhi arsalta (O Allah I submit my face to You, and I entrust my affairs to You, and I rely totally on You in hope and in fear of You. Verily there is no refuge nor safe haven from You except with You. O Allah, I believe in Your Book which You have revealed and in Your Prophet whom You have sent).  
Then if you die during the night, you will have died following the fitrah (sound nature of man). Make these the last words that you speak.” 
He said: I repeated it back to the Prophet (peace and blessings of Allah be upon him), and when I reached the words. “Allahumma aamantu bi kitaabika Allahi anzalta (O Allah, I believe in Your Book which You have revealed),” I said: “Wa rasoolika (And Your Messenger).” He said: “No. Wa nabiyyika alladhi arsalta (and Your Prophet whom You sent).” 
Narrated by al-Bukhari, 224; Muslim, 2710. 
It says in Tuhfat al-Ahwadhi: 
The scholars spoke about the Prophet (peace and blessings of Allah be upon him) correcting him and teaching him the correct wording. Al-Haafiz said: The best that can be said concerning the reason why the Prophet (peace and blessings of Allah be upon him) corrected the one who said Rasool (Messenger) instead of Nabi (Prophet) is that the wording of dhikrs is something that is to be recited as laid down in sharee’ah, and they have special characteristics which cannot be approximated, so they must be memorized with the wording in which they were narrated. This is the view favoured by al-Maazari who said: We should limit ourselves to the exact wording as it was narrated. The reward may be connected to this precise wording; perhaps they were revealed to him in that wording and must be recited in that specific form. End quote. 
There follows a number of du’a’s that were narrated from the Prophet (peace and blessings of Allah be upon him), which he used to recite during his prayer. 
1 –After the opening takbeer of the prayer and before starting to recite al-Faatihah. This is called du’a’ al-Istiftaah (opening supplication): 
It was narrated that Abu Hurayrah said: When the Messenger of Allah (peace and blessings of Allah be upon him) started to pray, he would remain silent for a while. I said: “May my father and mother be sacrificed for you, O Messenger of Allah. What do you say when you are silent between the takbeer and recitation?” He said: “I say: Allahumma baa’id bayni wa bayna khataayaaya kama baa’adta bayna al-mashriqi wa’l-maghrib. Allahumma naqqini min khataayaaya kama yunaqqa al-thawb al-abyad min al-danas. Allahumma ighsilni min khataayaaya bi’l-thalji wa’l-maa’i wa’l-barad    (O Allah, put a great distance between me and my sins, as great as the distance You have made between the East and the West. O Allah, cleanse me of sin as a white garment is cleansed from filth. O Allah, wash away my sins with snow and water and hail).” 
Narrated by al-Bukhari, 711; Muslim, 598. 
2 – du’a’ al-Qunoot in Witr 
It was narrated that al-Hasan ibn ‘Ali said: The Messenger of Allah (peace and blessings of Allah be upon him) taught me words to say in Witr: “Allahumma 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’aalayt (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).” 
Narrated by al-Tirmidhi, 464; al-Nasaa’i, 1745; Abu Dawood, 1425; Ibn Maajah, 1178. 
This hadith was classed as hasan by al-Tirmidhi and others, and as saheeh by al-Albani in Irwa’ al-Ghaleel, 429. 
3 – During bowing and prostration, the Messenger of Allah (peace and blessings of Allah be upon him) used to say: “Subhaanak Allahumma Rabbanaa wa bi hamdika Allahumma ighfir li (Glory and praise be to You, O Allah our Lord. O Allah, forgive me).” 
Narrated by al-Bukhari, 761; Muslim, 484, from the hadith of ‘Aa’ishah. 
Saying du’a’ whilst prostrating is the best of du’a’, because the Prophet (peace and blessings of Allah be upon him) said: “The closest that any one of you may be to his Lord is when he is prostrating, so say a lot of du’a’ at that time.” Narrated by Muslim, 482. 
4 – Between the two prostrations, he used to say: “Allahumma ighfir li warhamni wajburni wahdini warzuqni (O Allah, forgive me, have mercy on me, enrich me, guide me and grant me provision).”  
Narrated by al-Tirmidhi, 284; Ibn Maajah, 898; classed as saheeh by al-Albani in Saheeh al-Tirmidhi. 
5 – After the tashahhud and before the salaam: 
It was narrated from Abu Hurayrah that the Prophet (peace and blessings of Allah be upon him) said: “When any one of you has finished the last tashahhud, let him seek refuge with Allah from four things and say: Allahumma inni a’oodhu bika min ‘adhaabi jahannam wa min ‘adhaab il-qabri wa min fitnat il-mahyaa wa’l-mamaat wa min sharri fitnat il-maseeh il-dajjaal (O Allah, I seek refuge with You from the torment of Hell and from the torment of the grave and from the trials of life and death and from the evil of the trial of the Dajjaal).” Narrated by al-Bukhari, 1311; Muslim, 588 – this version narrated by Muslim). 
Al-Bukhari (834) and Muslim (2705) narrated from Abu Bakr al-Siddeeq that he said to the Messenger of Allah (peace and blessings of Allah be upon him): “Teach me a du’a’ that I may say in my prayer.” He said: “Say: ‘Allahumma inni zalamtu nafsi zulman katheeran wa laa yaghfir ul-dhunoob illa anta, faghfir li maghfiratan min ‘indaka warhamni, innaka anta al-Ghafoor al-Raheem (O Allah, indeed I have wronged myself greatly, and there is none who forgives sins besides You. So grant me forgiveness from You and have mercy on me, for you are the All-Forgiving, Most Merciful).’”  
Muslim (771) narrated a hadith which includes some of the du’a’s that the Prophet (peace and blessings of Allah be upon him) used to recite in his prayer. It was narrated from ‘Ali ibn Abi Taalib that when the Messenger of Allah (peace and blessings of Allah be upon him) stood up to pray, he would say:  
“Wajjahtu wajhiya lilladhi fatara al-samawaati wa’l-ard haneefan musliman wa maa ana min al-mushrikeen. Inna salaati wa nusuki wa mahyaaya wa mamaati Lillaahi Rabb il-‘Aalameen, laa shareeka lahu wa bidhaalika umirtu wa ana awwal ul-muslimeen, Allahumma anta al-malik laa ilaaha illa anta, anta rabbi wa ana ‘abduka. Zalamtu nafsi wa’tarafty bi dhanbi, faghfir li dhunoobi jamee’an, innahu laa yaghfir ul-dhunooba illa anta. Wahdini li ahsan al-akhlaaq la yahdi li ahsaniha illa anta. Wasrif ‘anni sayyi’aha laa yasrifu ‘anni sayyi’aha illa anta. Labbayka wa sa’dayka wa’l-khayra kulluhu fi yadayka wa’l-sharru laysa ilayka, ana bika wa ilayka, tabaarakta wa ta’aalayta, astaghfiruka wa atoobu ilayk… (I have set my face towards the Originator of the heavens and the earth sincerely [in Islam], and I am not among the Mushrikeen. Indeed, my prayer, my sacrifice, my living and my dying are for Allah, the Lord of the Worlds, no partner has He. With this I have been commanded and I am the first of the Muslims (those who submit to Him). O Allah, you are the King and there is no god but You. You are my Lord and I am Your slave. I have wronged myself, and have acknowledged my sins, so forgive all my sins, for no one forgives sins except You. Guide me to the best of attitudes, to which no one can guide except You, and save me from the worst of attitudes, from which no-one can save except You. I am here and happy to serve you. All good is in Your Hands, and evil is not from You. There is no escape or shelter from You except with You. Blessed are You  and exalted. I seek Your forgiveness and repent to You).” 
When he bowed he would say: “Allahumma laka raka’tu wa bika aamantu wa laka aslamtu, khasha’a laka sam’i wa basari wa mukhkhi wa ‘azmi wa ‘asabi (O Allah, to You have I bowed, in You have I believed and to You have I submitted. My hearing, sight, mind, bones and tendons are humbled before You).” 
When he stood up he would say: “Allahumma rabbana laka al-hamd mil’ al-samawaati wa mil’ al-ard wa mil’a ma baynahuma wa mil’a ma shi’ta min shay’in ba’d (O Allah our Lord, to You be praise filling the heavens, filling the earth, filling everything in between and filling whatever else You will besides that). 
When he prostrated he would say: “Allahumma laka sajadtu wa bika aamantu wa laka aslamtu. Sajada wajhi lilladhi khalaqahu wa sawwarahu wa shaqqa sam’ahu wa basarahu, tabaaraka Allahu ahsan al-khaaliqeen (O Allah! For you I have prostrated, in You I have believed and to You I have submitted. My face has prostrated for the One Who created it and shaped it, then brought forth its hearing and vision. Blessed be Allah, the Best of creators).” 
Then the last thing that he said between the tashahhud and the tasleem was: 
“Allahumma ighfir li ma qaddamtu wa ma akhkhartu wa ma asrartu wa ma a’lantu wa ma astraftu wa ma anta a’lamu bihi minni. Anta al-muqaddim wa anta al-mu’akhkhir laa ilaaha illa anta (O Allah! Forgive me what I have done in the past, and what I will do in the future, and what I have concealed, and what I have done openly, and what I have exceeded in, whatever You know about me more than I. You are the One Who brings forward, and You are the One Who puts back, there is no god except You).” 
And Allah knows best.