As Jewish couples contemplate "setting their date," it might help them to know the times of the year or specific days that the local rabbis will not be able to perform the ceremony -- and even the time of year that Jewish tradition has considered most favorable.
There are two kinds of conflicts that preclude using certain days on the calendar for a Jewish wedding. One is on days that are already holidays, days already set aside for simcha and/or observance which would overshadow any wedding and therefore are not considered proper. Such days are Shabbat, the High Holy Days and Pesach, Shavuot and Sukkot. In the case of Shabbat, for traditional Jews, the work involved in preparation would also preclude using that day.
Some people include the 10 days between Rosh Hashana and Yom Kippur because the festive mood of weddings conflicts with the penitential mood of these days.
The cases of two other holidays, Chanukah and Purim, are different. There is a dispute in Jewish legal sources as to whether a wedding on Purim is permitted or not, but most of the rabbis queried agreed that it rarely comes up. Weddings are permitted on Chanukah.
The other conflict is those times of year that are traditionally considered national mourning periods. The chief day of mourning is the ninth of Av, the date that both Temples in Jerusalem were destroyed. No local rabbis perform marriage ceremonies on that date.
Most people also exclude the three weeks of mourning that precede this fast day and continue through the fast day of the 17th of Tammuz, the day the walls of Jerusalem were breached. We are now in the period of three weeks, which began July 8 and end on July 29.
Sefira, the period of counting the days between Passover and Shavuot, is a mourning period that occurs in the spring. Different sects of Jews have differing customs of when they observe sefira, but none of them marry during this period. One widely accepted tradition is from Passover until Lag B'Omer, excluding both Yom Ha Atzma'ut, Israel Independence Day, and Rosh Chodesh Iyar (the first day of the month of Iyar, as first days are considered traditional minor holidays).
For example, the Lithuanian custom was to begin with Rosh Chodesh Iyar (eight days after Pesach ends) and go until three days before the start of Shavuot, with the exclusion of Lag B'Omer. Sephardic and Chassidic Jews generally observe sefira from the second day of Pesach until Lag B'Omer, but Chabad goes straight from the end of Passover to Shavuot.
In Israel, the chief rabbis have declared that weddings are permitted on both Independence Day and Jerusalem Day -- the day of the reunification of Jerusalem after the '67 War. The great halachic authority Rabbi Moshe Feinstein declared that one could be lenient about choosing which custom of sefira one observed.
In terms of particularly good times to get married, some rabbis like to perform weddings in the Hebrew month of Elul because it can be read as an acronym for the Hebrew words Ani l'dodi vdodi li (I am my beloved's, and my beloved is mine).
The month of Elul in the Hebrew calendar is the month that precedes Rosh Hashana.
Others suggest that Rosh Chodesh is considered a particularly auspicious day to marry.
Many believe that Tuesdays are prosperous days because in the story of creation in Genesis, it is written twice about that day that "God saw it was good." Also, because the Jewish people are compared to the moon, it was customary to get married in the first half of the lunar month, when the moon is waxing, not waning.
Second marriages are often conducted on Thursdays, because it gives the couple a long weekend together before resuming their everyday life.
For first marriages, there is a custom of sheva brakhot, festive gatherings for the week after the marriage, with special meals, and the wedding blessings recited at each gathering. During this period neither bride nor groom work, but are expected to amuse each other and have their friends amuse them. Second marriages do not customarily follow the sheva brakhot pattern, but if one gets married on Thursday, then it is reasonable to have Friday off and prepare for Shabbat together, and so the couple has more celebratory time together.
The months of Adar and Nissan were considered auspicious by the rabbis: Adar because it says in the Talmud that when Adar comes we multiply joy; Nissan because the rabbis see it as the month of redemption.
One more day mentioned, at least in the Talmud, as propitious is the 15th of Av, called "Tu B'av." In the time of the First Temple, it was a day for rejoicing, dancing and matchmaking. In Chassidic thought, getting married after the ninth of Av carries a certain appropriateness: the proper response to the ninth of Av, a day of destruction, is seen as construction of a new house in Israel.
Even though there are days on the Jewish calendar when marriages are not permitted, there are no days when engagement is prohibited.