This tkhine is to be recited when the Sefer Torah is taken out.
On Rosh Hashanah one should say the following, three times:
 
YHVH,
YHVH El, gracious and compassionate,
patient,
abounding in kindness and faithfulness,
assuring love for a thousand generations,
forgiving iniquity, transgression, and sin,
and granting pardon.”^[1] Exodus 34:6-7.  

Master of the Cosmos, I depend upon your thirteen attributes which are purest compassion. I stand before you and beseech your Holy Name, that just as we open the door of the Aron haḲodesh to take out the holy Sefer Torah, so will you open your gates of compassion and forgive us our sins which we have committed against you. Just as we have dressed your holy Sifrei Torah in white mantles,^[2] Per custom. Compare with the custom of wearing a white kittle.   so may you make white the stains upon our souls that we have stained with our sins. As the verse says: ‘Though your sins be like scarlet threads, I will make them white.”^[3] Cf. Isaiah 1:18  

Master of the Cosmos, just as we now take out the Torah, which is called a holy book, so may you inscribe us today in the Book of Life and in the Book of Blessing.^[4] Mishnah Avot 2:1   We are now about to read in your Sefer Torah how you heard Sarah’s prayer on Rosh Hashanah.^[5] Cf. Rosh Hashanah 10b-11a. Hashem decreed on Rosh Hashanah that Sarah, Rivqah, and Ḥannah would conceive and give birth.   We will also read in the haftarah how you heard the prayer of your righteous Ḥanah. So may you also hear our prayers today. Just as you freed your servant Yosef from prison on Rosh Hashanah,^[6] Louis Ginzberg, Legends of the Jews, vol. 5, p. 343, note on vol. 2, p.169: “According to old sources, Joseph left the prison on New Year. Comp. Rosh haShanah 11a; Tehillim 81, 368; Targum Psalms 81:6.”   so may you also free us on this Day of Judgment. You have written in your holy Torah that none of your gates is ever locked, so that you may hear our prayers and lamentations. Therefore, hear our plea. Inscribe us for a healthy year. And may you not, [G!D] forbid, take us away from this world before we are seventy years old,^[7] Cf. Psalms 90:10   so that we will not, [G!D] forbid, leave young orphans behind. May we be able to raise our children so that they will study your holy Torah for your Holy Name’s sake. And may you also not take our children away during our lifetime. You have also written for us in the Torah that we should honor our father and mother in their old age. Therefore, dear merciful Father, we weep and beseech you not to, [G!D] forbid, take away our little children in our lifetime. Father, merciful God, we fall upon our faces and beg you not to take away our husbands, for you have written: “I will mourn very bitterly, as a woman mourns for her husband.”^[8] Cf. 2 Samuel 14   Therefore, Master of the Cosmos, I beg you not to separate us from one another. Merciful Father, we beg you not to, [G!D] forbid, take away our brothers and sisters, for our tears would then bore a hole under your holy throne. May our prayers come into your hand.

We also ask the Sifrei Torah, which are now being taken out, to be advocates on our behalf. And may the Satan not accuse us, and may the attribute of mercy support our deeds. We beseech you, holy Sifrei Torah, even though we have not observed many of the mitsves which are written within you, nevertheless, we depend upon the verse as it is written, that a time will come when God will forgive the sins of Yisro’el.^[9] Cf. Micah 7:18-19   Therefore, we beseech you, that today should be the day for you to forgive our sins, as it is written in your holy Torah: “There is nothing which cannot be forgiven through repentance.”^[10] Genesis Rabbah 44:15   Merciful Father, we now break our hearts into thirteen pieces in accordance with your thirteen attributes. We will sin no more. Forgive our sins. Your holy prophets said to Yisro’el: “There will come a time when the righteous Moshiaḥ will come and redeem us.” Therefore we pray that you affirm their words. May you give us bounty and blessing from your holy hand, so that we will not, [G!D] forbid, need to depend upon mortals for assistance. Amen, selah.