There is no special dua for each lap of sa‘i. Say the authentic dhikr on Safa and Marwah, then make any dua you like. Below are the Sunnah first, followed by comprehensive duas of the Prophet ﷺ.
Innas-Safa wal-Marwata min sha‘a’irillah. Abda’u bima bada’allahu bih. Allahu akbar (3). La ilaha illallahu wahdahu la sharika lah, lahul-mulku wa lahul-hamdu wa huwa ‘ala kulli shay’in qadir. La ilaha illallahu wahdah, anjaza wa‘dah, wa nasara ‘abdah, wa hazamal-ahzaba wahdah.
"Indeed Safa and Marwah are among the symbols of Allah." I begin with what Allah began with. Allah is the Greatest (3). There is no god but Allah alone, with no partner; His is the dominion and His is the praise, and He has power over all things. There is no god but Allah alone; He fulfilled His promise, gave victory to His servant and defeated the confederates alone.
Recite the verse only when first climbing Safa. Face the Ka‘bah, raise your hands, say the dhikr three times and make dua between each time. Do the same on Marwah.
My Lord, forgive and have mercy; You are the Most Mighty, the Most Generous. This was said during sa‘i by the Companions ‘Abdullah ibn Mas‘ud and ‘Abdullah ibn ‘Umar.
Reference: Ibn Abi Shaybah, al-Musannaf (authentic as the saying of the Companions)
2. Comprehensive duas of the Prophet ﷺ and from the Quran
Choose any of these during sa‘i, on the Day of Arafah or any time. Each is from the Quran or an authentic hadith.
Rabbana atina fid-dunya hasanatan wa fil-akhirati hasanatan wa qina ‘adhaban-nar.
Our Lord, give us good in this world and good in the Hereafter, and protect us from the punishment of the Fire. (The dua the Prophet ﷺ made most often.)
Allahumma inni a‘udhu bika minal-hammi wal-hazan, wal-‘ajzi wal-kasal, wal-bukhli wal-jubn, wa dala‘id-dayni wa ghalabatir-rijal.
O Allah, I seek refuge in You from worry and grief, from weakness and laziness, from miserliness and cowardice, from the burden of debt and from being overpowered by men.
Allahumma aslih li diniyalladhi huwa ‘ismatu amri, wa aslih li dunyayallati fiha ma‘ashi, wa aslih li akhiratiyallati fiha ma‘adi, waj‘alil-hayata ziyadatan li fi kulli khayr, waj‘alil-mawta rahatan li min kulli sharr.
O Allah, set right my religion which is the safeguard of my affairs, set right my worldly life in which is my living, and set right my Hereafter to which is my return. Make life an increase for me in every good, and make death a relief for me from every evil.
Allahumma inni as’aluka minal-khayri kullihi, ‘ajilihi wa ajilihi, ma ‘alimtu minhu wa ma lam a‘lam, wa a‘udhu bika minash-sharri kullihi, ‘ajilihi wa ajilihi, ma ‘alimtu minhu wa ma lam a‘lam. Allahumma inni as’alukal-jannata wa ma qarraba ilayha min qawlin aw ‘amal, wa a‘udhu bika minan-nari wa ma qarraba ilayha min qawlin aw ‘amal, wa as’aluka an taj‘ala kulla qada’in qadaytahu li khayra.
O Allah, I ask You for all good, sooner and later, what I know of it and what I do not know, and I seek refuge in You from all evil, sooner and later, what I know of it and what I do not know. O Allah, I ask You for Paradise and whatever word or deed brings one near to it, and I seek refuge in You from the Fire and whatever word or deed brings one near to it, and I ask You to make every decree You decree for me good.
Reference: Ibn Majah 3846 (graded sahih by al-Albani)
Allahumma inni a‘udhu bika min ‘ilmin la yanfa‘, wa min qalbin la yakhsha‘, wa min nafsin la tashba‘, wa min da‘watin la yustajabu laha.
O Allah, I seek refuge in You from knowledge that does not benefit, from a heart that does not humble itself, from a soul that is never satisfied, and from a supplication that is not answered.
Allahummaghfir li khati’ati wa jahli, wa israfi fi amri, wa ma anta a‘lamu bihi minni. Allahummaghfir li jiddi wa hazli, wa khata’i wa ‘amdi, wa kullu dhalika ‘indi.
O Allah, forgive my sins, my ignorance, my excess in my affairs and what You know better than me. O Allah, forgive what I did seriously and in jest, by mistake and on purpose, and all of that is in me.
Allahumma inni a‘udhu bika minal-‘ajzi wal-kasal, wal-jubni wal-harami wal-bukhl, wa a‘udhu bika min ‘adhabil-qabr, wa min fitnatil-mahya wal-mamat.
O Allah, I seek refuge in You from weakness and laziness, cowardice, old age and miserliness, and I seek refuge in You from the punishment of the grave and from the trials of life and death.
Rabbana taqabbal minna innaka antas-Sami‘ul-‘Alim, wa tub ‘alayna innaka antat-Tawwabur-Rahim.
Our Lord, accept this from us; You are the All-Hearing, the All-Knowing. And accept our repentance; You are the Accepter of repentance, the Most Merciful. (Said while raising the foundations of the Ka‘bah.)
Rabbij‘alni muqimas-salati wa min dhurriyyati, Rabbana wa taqabbal du‘a’. Rabbanaghfir li wa li walidayya wa lil-mu’minina yawma yaqumul-hisab.
My Lord, make me one who establishes prayer, and from my descendants. Our Lord, accept my supplication. Our Lord, forgive me, my parents and the believers on the Day the account is established.
Allahumma anta Rabbi la ilaha illa ant, khalaqtani wa ana ‘abduk, wa ana ‘ala ‘ahdika wa wa‘dika mastata‘t, a‘udhu bika min sharri ma sana‘t, abu’u laka bi ni‘matika ‘alayya, wa abu’u laka bi dhanbi faghfir li, fa innahu la yaghfirudh-dhunuba illa ant.
O Allah, You are my Lord; there is no god but You. You created me and I am Your servant, and I keep Your covenant and promise as best I can. I seek refuge in You from the evil of what I have done. I acknowledge Your favour upon me and I acknowledge my sin, so forgive me, for none forgives sins but You.
