Tachanun is omitted on Pesach Sheiyni, which is the 14th of Iyar. It is however recited the Mincha prior, on the 13th of Iyar. [Thus when the 13th falls on Shabbos, Tzidkascha is recited by Mincha.] Tachanun is likewise omitted on the night of the 14th in Kerias Shema Sheal Hamita. It is questionable whether it is to be recited on Motzei Pesach Sheiyni, which is the night of the 15th. [However on the day of the 15th Tachanun is recited.]
 Siddur Admur; Siddur Shlah; Elya Raba 131/14; Shalmei Tzibur p. 151; Siddur Yaavetz; Shaareiy Efraim 10/27; Ashel Avraham Butchach 131; Divreiy Nehemiah 131; Not listed in Shulchan Aruch chapter 131. See Aruch Hashulchan 131/12 and Yalkut Avraham 493 which wonders at this matter.
Other Opinions: Some Poskim rule that Tachanun is to be recited on Pesach Sheiyni. [P”M 131 M”Z 14; Noam Megadim 26; custom of Chazon Ish; This was the widespread Ashkenazi custom] It is interesting to note that one of the main claims of the Misnagdim against the Chassidim in the Cherem of 1772 was that they did not say Tachanun on Pesach Sheiyni, and held feasts on the day even when it fell on Behab. [Nitei Gavriel Pesach 3 57/3]
 Siddur Admur; Divreiy Nehemiah 131; Hayom Yom 13th Iyar
Other Opinions: Some Poskim rule that Tachanun is omitted also from the Mincha prior. [Shaar Yissachar Pesach Zeira in name of Arizal; Nitei Gavriel 57/4 in name of Sefarim; Siddur Arizal Chemdas Yisrael]
 Hiskashrus 1033
 Sichas 1983 Pesach Sheiyni letter 12; Behar Bechukosaiy 1983 letter 42; See Otzer Minhagei Chabad Iyar 42
 Rebbe ibid; Machazik Bracha 131/4; Beis David 53; Shaareiy Teshuvah 131/19
Other opinions: Some are accustomed not to say Tachanun also on the 15th. [Shalmei Tzibur p. 151; See Otzer Minhagei Chabad p. 267; Regarding the opinion of the Munkatcher, in Darkei Chaim Veshalom 191 it states that he did not say Tachanun, while in Shaar Yissachar [Pesach Zeira] he writes that according to the Arizal one does say Tachanun. The Rebbe ibid explains that most likely the Munkatcher held Tachanun is omitted by the night of the 15th and not the day.]
Custom to omit Tachanun for seven days: Some are accustomed to omit Tachanun for seven days until the Tashlumin of Pesach Sheiyni expires.