Are male children of Chinuch age obligated to recite Sefiras Haomer:
Children below the age of Chinuch: A child who is below the age of Chinuch is exempt from all Mitzvos.
Above age of Chinuch by Shema and other night Mitzvos: A son who has reached the age of Chinuch is obligated to be educated by his father in the fulfillment of all Mitzvos. This applies even by Mitzvos they are to be fulfilled at night. Some Poskim, however, rule that even by a son who has reached the age of Chinuch, the father is exempt from educating him to recite Kerias Shema and its blessings being that it is a night Mitzvah. Practically, it is proper to follow the first opinion. The above is only regarding the Shema and its blessings, however, regarding Shemoneh Esrei, the father is obligated to educate his son to Daven Shemoneh Esrei both by night [Maariv] and day. [Accordingly, it is proper for a father to make sure that his son recites the morning Shema before Sof Zman Kerias Shema, and that he Davens the entire Maariv, from when he reaches the age of Chinuch. Some Poskim rule that once a son has reached the age of 12, the father is obligated to educate him in saying Shema according to all.]
Definition of age of Chinuch: The age of Chinuch is from the age that the child understands the meaning of the Mitzvah. [This is approximately from age 6-7. Other Poskim rule it is between age 9-10. Practically, it all depends on the child’s maturity.]
B. The law:
A child who is below the age of Chinuch is exempt from counting Sefiras Haomer, as is the law by Mitzvos. Furthermore, it is disputed if even male children who have reached the age of Chinuch must be educated to recite Sefiras Haomer. Practically, the Poskim conclude that children who have reached the age of Chinuch are to be educated in the Mitzvah of Sefiras HaOmer. They are to recite it at night with a blessing [if they have not missed a previous night], following the same laws as adult men. The age of Chinuch is from the age that the child understands the meaning of Sefiras Haomer.
Once a child has reached the age of Chinuch, it is proper to educate him in the saying of Sefiras Haomer at night with its blessing.
In areas that night begins very late, must one keep the child awake until late at night in order to say Sefiras Haomer?
It is proper to wake the child up after night in order to say Sefira. This applies only if the child has reached the age of Chinuch. If this poses difficulty, one may simply recite Sefira with the child during the day.
 See Admur 70:2; 343:3
 Admur 343:3
 Stam opinion in Admur 70:2; 1st opinion in Michaber 70:2; Rabbeinu Tam in Tosafus Brachos 20a; Rosh Brachos 3:13
 2nd opinion in Admur ibid; 2nd opinion in Michaber 70:2; Rashi Brachos 20a
 The reason: The Sages did not impose on the father to educate a child to recite Shema and its blessings, being that the father is not found together with his child during the time of Kerias Shema at night, and by morning the child is still sleeping. [Admur ibid] See Biur Halacha 70:2 “Ketanim Peturim” who questions Admur as to why Admur exempts educating the child in the blessings of Shema, if the blessings may be recited until late. He explains that if the father is exempt from educating the son in the Biblical command of Shema, then certainly he is exempt from Birchas Shema.
 Admur ibid; Michaber ibid
 Admur ibid “Erev Vaboker”; M”B 106:5; Salmas Chaim 36; Piskeiy Teshuvos 107:2 hat this refers to Maariv [and not Mincha], so is evident from both the wording and the fact Admur writes it prior to Boker.
 Admur 106:3; Michaber 106:1; Mishneh Brachos 20a
 Bach 70; M”B 70:8
 Admur 343:3
 M”B 70:6
 Kesher Gudal 11:1; Shalmei Tzibur
 Kaf Hachaim 70:6
 See Admur 70:2; 343:3
 Regarding Mitzvos that apply in early morning or at night, during hours a child might not be awake, see Admur 70:2 regarding Shema that this matter is disputed in Poskim; See M”B 426:1 that states this dispute regarding Shema would likewise apply regarding Kiddush Levana, and accordingly, the same should apply regarding Sefiras Haomer. Vetzaruch Iyun, as there are night mitzvah’s in which according to all opinions the sages obligated the father to educate his children in their performance such as Maariv [see Admur 70:2], and Kiddush and Havdalah [Admur 343:3], and perhaps Sefiras Haomer has a similar ruling. Vetzaruch Iyun as to how to determine the night Mitzvos that the second opinion exempts from and the ones that they obligate! To note, that according to those who rule that the Mitzvah of Sefira applies also by day, this dispute is irrelevant, and one is obligated to educate his child in Sefira according to all.
Opinions who obligate regarding Shema: Stam opinion in Admur 70:2; 1st opinion in Michaber 70:2; Rabbeinu Tam in Tosafus Brachos 20a; Rosh Brachos 3:13
Opinions who exempt regarding Shema: 2nd opinion in Admur ibid; 2nd opinion in Michaber 70:2; Rashi Brachos 20a
 Admur 343:2-3 regarding all Mitzvos, and in accordance to 1st opinion in Admur 70:2 and final ruling there that even by night Mitzvos one should follow the first, stringent, opinion [see previous footnote]; Shaareiy Teshuvah 489:20 “Our custom is that children who have reached the age of Chinuch count with a blessing”; Maharil Hilchos Sefiras Haomer
Other opinions: Seemingly, according to those opinions who exempt educating children in the recital of Shema at night due to that the father is not found with them at night then seemingly the same would apply regarding Sefiras Haomer, that the father would be exempt from educating them to recite it. [See Admur 70:2 and Michaber 70:2 and Rashi Brachos 20a regarding Shema; See M”B 426:1 that states this dispute regarding Shema would likewise apply regarding Kiddush Levana, and accordingly, the same should apply regarding Sefiras Haomer.]
 As is the law by an adult; However, see Nitei Gavriel 24:7 footnote 13 who novelizes that they may continue to count with a blessing, and so rules Rav Yaakov Yosef and Rav Gershon Lapidos, Rav of Beis Yisrael, based on Admur 215:2; Michaber 215:3; Rambam Brachos 1:15 that Bracha Levatala does not apply to children. However, seemingly, due to reasons of Chinuch one should educate the child not to say a blessing, so he be educated in the when he is older.
 Admur 343:3
 See Admur 70:2 regarding Shema