1) Some have the custom not to bless the new moon until the night after Yom Kippur, as then we are happy, whereas earlier we are worried because of the fear of the judgment. Others have the custom to say it earlier in order to have more merits for Yom Kippur. (Kitzur Shulchan Aruch 130)
2) Men of deeds have the custom to hurry to buy the four species during the ten days of repentance so that this precious commandment will also be added on to their merits. (ibid)