Is it possible to have a stone setting on 7th Av - Fast of Gedaliah and just before Tisha BAv?

ב"ה ב"ה Shalom First of all , there are different customs regarding the unveiling of the tombstone. Some have the custom to erect the monument immediately after the Shivah or at least be completed by the Shloshim. While others rule it should be erected after the 12 months of mourning. (See Mourning in Halacha 41:2). You should follow your local custom. Since the custom is to eulogize when erecting the monument, some have the custom of not erecting the monument on days Tachanun isn't said. None of the above dates: the 7th of Av, 8th of Av which is just before Tishah B'av , Fast of Gedalya which on the 3rd of Tishrei, right after Rosh Hashana, are dates upon which Tachanun is not said. Therefore, there is no problem of erecting the monument on them. (See Mourning in Halacha 41:9 note 16). However, some say that the erecting of the monument, should not place 30 days before a festival. Therefore, some would say that on Fast of Gedalya which on the 3rd of Tishrei, which is under two weeks before Sukkot, the monument should not be erected. However, since customs change from place to place you should be in touch with local Rabbi or Chevra Kadisha= burial services, to verify the local custom. All the best