Is there a proper greeting for the Three Weeks and Tisha B'av? For some reason "goodday" or "shalom aleichem" don't seem like good greetings for a period of mourning.
Based on (O.C. 554:21) אֵין שְׁאֵלַת שָׁלוֹם לַחֲבֵרוֹ בְּתִשְׁעָה בְּאָב, וְהֶדְיוֹטוֹת שֶׁאֵינָם יוֹדְעִים וְנוֹתְנִים שָׁלוֹם, מְשִׁיבִים לָהֶם בְּשָׂפָה רָפָה וּבְכֹבֶד רֹאשׁ,
Rav Ari Enkin concludes his article saying,
While it may just be that those who choose to be strict and not offer any greeting whatsoever when in mourning or on Tisha B'av are following a preferred course, it cannot be suggested that a simple social acknowledgment is in violation of halacha. Those who feel that it is rude or uncomfortable to pass others without an acknowledgement of some sort should feel free to offer a somber "hello" without reservation.[Be'er Moshe 4:106] Often merely saluting another person in a somewhat formal manner and tone of voice ("Mr. Levine") accomplishes the same thing as well.
Although Guidelines (Q:263) writes not to nod in greeting on Tisha B'Av, this pamphlet put out by the Agudah (p26) writes
Nodding and Waving are Permissible