Praise be to Allah.
“Supplication is worship,” as the Prophet (blessings and peace of Allah be upon him) said; narrated by at-Tirmidhi and others with a saheeh isnaad. The basic principle with regard to acts of worship is tawqeef (i.e., it is not permissible to worship Allah, may He be exalted, through any act of worship unless this act of worship is proven in the shar‘i texts (Qur’aan and Sunnah) to be an act of worship that was prescribed by Allah) and disallowance (of anything that is not expressly prescribed). Therefore it is not permissible to invent acts of worship or to limit them to a particular time or occasion, unless the Islamic teachings indicate that.
So it is not permissible for anyone to prescribe for the people supplications to be said at specific times.
Supplication (du‘aa’) during Ramadan is encouraged, but this encouragement does not make it permissible for anyone to make up supplications by himself and say that they are to be recited at specific times, as if they are Prophetic supplications. Rather the Muslim may offer supplication for whatever he likes of good in this world and in the Hereafter, in whatever words are easy for him, at any time.
An example of that is something that the scholars have warned against doing, but it is widespread among the common folk, namely reciting specific supplications in each circuit of tawaaf (circumambulation of the Ka‘bah) or lap of sa‘i (going between as-Safa and al-Marwah) during Hajj and ‘Umrah.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him) said:
It is not permissible in this tawaaf, or any other tawaaf, or in sa‘i, to recite a specific dhikr or a specific du‘aa’. As for what some people have invented of reciting specific dhikrs or du‘aa’s in each circuit of tawaaf and each lap of sa‘i, there is no basis for that; rather whatever one is able to say of dhikr and du‘aa’ is sufficient.
Fataawa ash-Shaykh Ibn Baaz (16/61, 62)
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said:
There is no specific du‘aa’ for each circuit (of tawaaf); rather specifying a particular du‘aa’ for each circuit is a kind of innovation (bid‘ah), because that was not narrated from the Prophet (blessings and peace of Allah be upon him). All that has been narrated is to say takbeer when touching the Black Stone, and to say “Rabbana aatina fi’d-dunya hasanatan wa fi’l-aakhirati hasanah wa qina ‘adhaab an-naar (Our Lord! Give us in this world that which is good and in the Hereafter that which is good, and save us from the torment of the Fire)” [al-Baqarah 2:201] between ar-Rukn al-Yamaani (the Yemeni Corner) and the Black Stone. As for the rest, it is dhikr, recitation of Qur’an and du‘aa’ in general terms, and there is nothing specific to be recited in one circuit and not another.
Majmoo‘ Fataawa ash-Shaykh al-‘Uthaymeen (22/336)
And another thing:
In the supplication for the last day, there is something that is reprehensible and contrary to Islamic teaching: namely tawassul (seeking to draw closer to Allah) in the supplication by virtue of the Prophet (blessings and peace of Allah be upon him) and by virtue of the members of his household.
We have previously explained that this kind of tawassul in supplication is bid‘ah (an innovation), and we have quoted the words of the scholars concerning it, in the answer to question no. 125339.
The Muslim should not participate in the propagation of this publication; rather he should warn against it to the best of his ability. The Muslim should understand that there is nothing good in innovations by means of which he seeks to draw closer to his Lord, for the Prophet (blessings and peace of Allah be upon him) said: “Every innovation is a going astray.” Narrated by Muslim (867).
And Allah knows best.