The Kedushat Levi says that each night of Chanuka is mesugal, an auspicious time for different things to daven / pray for:
1st night -not to be lonely or depressed
2nd night– Shidduchim, Shalom Bayis, to find your marriage partner and marital peace
3rd night- Good children, Happy children and healthy (Chasam Sofer ztk’l says when you cry in front of the candles you can be sure your tefilos / prayers are answered)
4th night– 4 lmahos / 4 Matriarchs – To be a healthy and wholesome woman/mother in the 4 walls of your home, of true essence
5th night — Chamisha Chumshei Torah, The Five books of Torah. Daven / Pray that your husband should be a ralmid chacham / Torah Scholar as well as your children. By the 5th night more of the menorah is lit up than not. Pray for more light in your life, for clarity.
6th night – Simcha / Happiness – You can have everything and still be sad, therefore pray for joy and happiness
7th night – Happy and Peaceful Shabbat – zmiros / Jewish Song Sing, Divrei Torah / Words of Torah said by your Seuda.Shabbat / Meal of Shabbat is the source of all berakha / blessing.
8th night– mesugal / auspicious time to pray for barren women. 8 is above nature, powerful day to pray.

Kedushat Levi says if you are planning to start something new, if you start it on Chanuka it will be blessed, Bezrat Hash-m / with the help of G-d.