It is customary to omit Tahanunim, and to instead recite Yehi Shem, in a synagogue where a Berit will be taking place. All the Minyanim in the synagogue omit Tahanunim on a day when a Berit is being performed there in the synagogue.
There is considerable discussion among the Halachic authorities as to whether this applies if the Berit is scheduled for the afternoon hours, well after the Shaharit prayers. For example, if the Berit will be taking place after Minha, are Tahanunim omitted even during Shaharit, or only during Minha?
Many Poskim, including the Nehar Misrayim, Beneh Yehuda Maslaton and Hacham Ovadia Hedaya (in Yaskil Abdi), as well as Hacham Ovadia Yosef, maintain that Tahanunim are recited in Shaharit in such a case. These Poskim compare this case to that of a Hatan who attends Shaharit in the morning and is getting married in the afternoon. The Hid"a (Rav Haim Yosef David Azulai, 1724-1807) ruled that Tahanunim are recited during Shaharit at the Minyan when the Hatan prays, since he is not getting married until much later in the day. According to the Hida, Tahanunim are omitted only in the prayer service immediately preceding the wedding. By the same token, when a Berit is being held in the synagogue, Tahanunim are recited only in the immediately preceding prayer, and thus if the Berit is performed after Minha, Tahanunim are omitted during Minha but recited during Shaharit. Although some Poskim rule otherwise, and maintain that Tahanunim are omitted even during Shaharit in such a case, the consensus among the authorities is that Tahanunim are recited at Shaharit, as documented by Hacham David Yosef, in his Halacha Berura (vol. 7).
Summary: If a Berit is performed in a synagogue after Shaharit, Tahanunim are omitted during Shaharit. If a Berit is performed in a synagogue after Minha, Tahanunim are omitted during Minha but are recited during Shaharit.
