Best time to make duas:

1. Between Adhan & Iqma

2. On Jumaah (betw. Magrib of Thursday & Friday)

3. If traveling

4. If it rains

5. Third portion of night (Tahajjud)

6. If you’re oppressed

7. If one is ill (ask them to pray for you)

8. In sajjuud (closest to Allah you are)

9. After finishing the Quran

10. Dua supplicating with dua of Yunus (prophet in the whale's stomach)-

Surah anbiya 21:87:

And (remember) Dhan-Nûn (Jonah), when he went off in anger, and imagined that We shall not punish him (i.e. the calamites which had befallen him)! But he cried through the darkness (saying): Lâ ilâha illa Anta [none has the right to be worshipped but You (O Allâh)], Glorified (and Exalted) are You [above all that (evil) they associate with You]. Truly, I have been of the wrong-doers."

Note: all time is for duaa bit its just best times.....