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The prayers said after the Sefira:[1]

After the counting of the Sefira it is customary to recite “Yehi Ratzon Sheyibaneh Beis Hamikdash etc”[2] (Some are accustomed for reasons known to them to say after this prayer the Psalm of “Elokim Yichaneinu Vivarcheinu”, Ana Bekoach, and Ribono Shel Olam.[3]) [Practically, so is the ruling of the Siddur and the Chabad custom. Some are accustomed to recite Lesheim Yichud or Hareini Muchan Umezuman prior to counting the Sefira.[4] This is not the Chabad custom.]

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[1] Admur 489:11; Tosafus Megillah 20b; Bach 489; Chok Yaakov 489:11; M”B 489:10; See Piskeiy Teshuvos 489:10

[2] The reason: being that in today’s times we are only counting in memory of the Mikdash, and the counting in it of itself does not constitute a Mitzvah at all. As the Mitzvah is to count from the Omer and today we do not have an Omer from which to count, and the Sages simply instituted the counting in memory of the Mikdash. Therefore we Daven to Hashem at this time that he builds the Beis Hamikdash and allow us to fulfill the Mitzvah properly. [ibid]

The Nussach: This is the dialect of Admur in the Shulchan Aruch ibid, however in the Siddur the Nussach is “Harachamn Hu Yachzir Lanu Avodas Beis Hamikdash Lemikomah Bemiheira Biyameinu Amen Selah.” This follows the wording of the Abudarham.

[3] Admur ibid in parentheses; based on Peri Eitz Chaim and Siddur Arizal; See Siddur of Rav Raskin footnote 18

Other opinions: Some Poskim severely negate the recital of these parts. [Chok Yaakov 489:11 based on Maharshal 98; Aruch Hashulchan 489:10]

[4] See Yesod Veshoresh Havoda 9:8; Mishmeres Shalom 36:2; Orchos Chaim 489:4; Shaar Yissachar Nissan Omer Hatenufa 17; Darkei Chaim Vehsalom 625; Dvar Moshe 29; Kaf Hachaim 489:7; Noda Beyehuda Kama Y.D. 93; Piskeiy Teshuyvos ibid footnotes 46-49