Q. See question above. Is it permitted to get engaged in the Nine Days and serve a Lechaim?
A. Magen Avraham 551:10 rules that it is permitted to become engaged and write tenaim during the Nine Days, even on Tisha BeAv itself, as long as there is no meal, music, or dancing. Until Rosh Chodesh, one is allowed to celebrate the engagement with a festive meal but without dancing. (Mishna Brurah 551: 19, Aruch Hashulchan 551:8, Yalkut Yosef Moadim page 553. )
However, the Tzitz Eliezer (13:60) notes that many Jews refrain from doing so on Tisha B'Av. In addition, the Ben Ish Chai (Devarim: Halacha 4) writes that in Baghdad, they would not get engaged during the Nine Days between Rosh Chodesh Av and Tisha B'Av. He says further that it is preferred not to get engaged at all during the "Three Weeks."
Rabbi A. Bartfeld as revised by Horav Y. Hirshman, Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu, Horav Kalman Ochs, and Horav Dovid Bartfeld consulting in need Horav Hagaon Rav Yitzchak Berkowitz Shlit’a