Reports indicating that he supplicated or delivered the sermon before the prayer

Abbad bin Tamim al-Mazini (may Allah have mercy on him) narrates that he heard his uncle (may Allah be pleased with him), who was one of the Companions of the Messenger of Allah (peace and blessings be upon him), say: One day the Messenger of Allah (peace and blessings be upon him) went out to supplicate for rain. He (peace and blessings be upon him) turned his back to the people and, facing the qiblah, supplicated to Allah Almighty, and he also turned his cloak around; then he (peace and blessings be upon him) prayed two rak'ahs. Ibn Abi Dhi'b said in this hadith that he (peace and blessings be upon him) also recited in them. Ibn Wahb (may Allah have mercy on him) said: By this he means that he (peace and blessings be upon him) recited aloud.
Also, Imam Bukhari (may Allah have mercy on him) recorded in his Sahih, by this same route, the hadith he narrated from Adam bin Abi Iyas from Ibn Abi Dhi'b. In it he said: He (peace and blessings be upon him) led us in two rak'ahs and recited aloud in them. A similar report is narrated from Abu Nu'aym (may Allah have mercy on him), which he narrated from Ibn Abi Dhi'b, and Imam Muslim (may Allah have mercy on him) narrated this hadith through the chain of Abu al-Tahir. Ma'mar narrated it from al-Zuhri, first describing the manner of the prayer, then mentioning the turning of the cloak and the supplication.

It is narrated from Sayyidah Aishah (may Allah be pleased with her) that the people complained to the Messenger of Allah (peace and blessings be upon him) about the lack of rain. He (peace and blessings be upon him) ordered a pulpit, and it was placed for him in the prayer ground (musalla), and he appointed a particular day for the people on which to come out. Sayyidah Aishah (may Allah be pleased with her) said: The Messenger of Allah (peace and blessings be upon him) came out when the edge of the sun appeared, and he (peace and blessings be upon him) sat on the pulpit and proclaimed Allah's greatness and praised Him. Then he (peace and blessings be upon him) said: "You have complained of the drought of your lands and of the rain being delayed beyond its due season, whereas Allah, Glorified and Exalted, has commanded you to call upon Him and has promised that He will answer your supplication." Then he (peace and blessings be upon him) said: 'Alhamdu lillahi Rabbil-'alamin, ar-Rahmanir-Rahim, Maliki yawmid-din, la ilaha illallahu yaf'alu ma yurid, Allahumma antallahu la ilaha illa antal-Ghaniyyu wa nahnul-fuqara', anzil 'alaynal-ghaytha, waj'al ma anzalta lana quwwatan wa balaghan ila hin' (All praise is for Allah, the Lord of all the worlds, the Most Gracious, the Most Merciful, Master of the Day of Recompense. There is no god but Allah; He does whatever He wills. O Allah, You are Allah, there is no god but You; You are the Self-Sufficient and we are the needy. Send down rain upon us, and make what You send down a source of strength for us and a provision for a while).
Then he (peace and blessings be upon him) raised his hands and kept them raised until the whiteness of his (peace and blessings be upon him) armpits became visible. Then he turned his back to the people and reversed his cloak while he (peace and blessings be upon him) was keeping his hands raised. Then he turned towards the people, came down from the pulpit and led two rak'ahs. Allah Almighty then produced clouds, which thundered and flashed with lightning, and then they rained by the command of Allah. He (peace and blessings be upon him) had not yet reached the mosque when the gutters began to flow. When he (peace and blessings be upon him) saw the people hurrying to take shelter from the rain, he (peace and blessings be upon him) smiled until his (peace and blessings be upon him) molar teeth became visible, and he (peace and blessings be upon him) said: "I bear witness that Allah Almighty has power over all things, and that I am His servant and Messenger."

It is narrated from Abu Ishaq that Abdullah bin Yazid al-Ansari (may Allah be pleased with him) went out to supplicate for rain, and he had seen the Prophet (peace and blessings be upon him). Among those who went out with him were al-Bara' bin Azib and Zayd bin Arqam (may Allah be pleased with them both). Abu Ishaq said: I too was with him that day. He stood on his feet, without a pulpit. Then he supplicated for rain and sought forgiveness, then he led us in two rak'ahs while we were behind him, reciting aloud in them; and he gave neither the adhan nor the iqamah. Imam Bukhari (may Allah have mercy on him) narrated this report in his Sahih from Abu Nu'aym. In what al-Thawri narrated from Abu Ishaq, he said: He delivered a sermon, then prayed. And in what Shu'bah narrated, it says that he prayed two rak'ahs, then supplicated.