One who is presented the opportunity to perform a mitzva that requires one to recite She-heĥeyanu, like a brit mila or a pidyon ha-ben, recites the berakha, because he did not determine the timing of the berakha. Rather, God granted him the opportunity to perform a mitzva that requires one to recite She-heĥeyanu during the Three Weeks (SA 551:17).
Similarly, one who sees a close friend after not seeing him for thirty days, and is happy to see him, should recite She-heĥeyanu, since if he does not recite it immediately, he loses the opportunity to recite the berakha. Likewise, one who sees his newborn daughter for the first time should recite She-heĥeyanu, since if he does not do so immediately, he loses the opportunity to recite the berakha (based on SA 225:1, MB 223:2).
According to most poskim, one may recite She-heĥeyanu on the Shabbatot of the Three Weeks. Even though some rule stringently on this issue (based on Arizal), in practice one may be lenient and recite She-heĥeyanu over a new fruit even on Shabbat Ĥazon (the Shabbat before Tisha Be-Av). Therefore, one who gets a new fruit during the week should postpone eating it until Shabbat, and then recite She-heĥeyanu over the fruit. If he cannot postpone eating it – for example, if he has no access to a refrigerator, and the fruit might spoil before Shabbat – he should eat it immediately and recite She-heĥeyanu (Rema 551:17, MB 551:98). With regard to a new article of clothing, one may likewise recite She-heĥeyanu on the Shabbatot before the first of Av. However, on Shabbat after the first of Av, one should be stringent and not wear the new garment, and thus not recite She-heĥeyanu (MB 551:98).