Are there any laws pertaining specifically for the 9 days between Rosh Chodesh and Tisha B’Av?
The Shulhan Aruch writes משנכנס אב ממעטין בשמחה – When Rosh Hodesh Av comes in, we minimize our happiness. This is due to the many calamities which have befallen the Jewish People during this time period. Therefore, certain things were prohibited through the 10th of Av. The following are some of those restrictions:
Avoiding Dangerous Activities
Hazal warn that one should refrain from certain dangerous activities during the time Ben Hametsarim. This includes walking alone in the outskirts of the city from the beginning of the fourth hour of the day until the end of the ninth hour, for there is an evil spirit (keteb meriri) which is found at these times that has permission to inflict damage.
Likewise, one should refrain from hitting children during the above time (although generally one should refrain from hitting their children throughout the year, this is especially true during these dangerous times).
Additionally, one should preferably delay a non-life-threatening surgery until after Tishaa b’Av.
Although one is permitted to go to the beach during Ben Hametsarim up until Shavuah Shehal Bo, one should be extra careful since there are many dangers found there.
Some are stringent to avoid unnecessary plane travel after Rosh Hodesh Av.
One should refrain from making parties and get-togethers from Rosh Hodesh Av. Some say that one may make a goodbye party for someone so long as it is not accompanied by music and a bread meal.
One who wishes to make a children’s birthday party at this time should seek out a competent halachic authority on how to orchestrate such an event.
One should refrain from purchasing an engagement ring during the nine days, since this is something that brings joy.
The accepted custom of many sefardic communities is to refrain from getting married from Rosh Hodesh Av until after Tishaa b’Av. This is unlike the prevalent ashkenzazic custom (and that of a few sefardic communities) to refrain already from the 17th of Tammuz.
A sefardic boy who marries an ashkenazic girl, may have their wedding from the 17th of Tammuz until Rosh Hodesh. This is even though the Ashkenzaic custom is to refrain from this time. Likewise, a sefardic girl who marries an Ashkenazic boy may not be lenient, but rather must wait to make the wedding after the three weeks as in all cases the custom of the man should be followed.
Although, the sefardic custom is to refrain from weddings from Rosh Hodesh until Tishaa b’Av, it is permitted to get engaged. However, one should refrain from making a party with a meal or music and dancing. Nevertheless, it is permitted to sing.
One should not delay from meeting a potential shidduch during this time.
 O.H. 551:1