There are certain times Dua is more likely to be accepted by Allah as mentioned by The Prophet (Peace Be Upon Him) Some of these times are as follows:-
1/ The last third of the night.
The Prophet (Peace Be Upon Him) said:- “When it is the last third of the night, Allah the Blessed, the Superior, descends every night to the heaven of the world and says, “Is there anyone (demand anything from Me), that I may respond to his invocation: Is there anyone who asks Me for something that I may give (it to) him? Is there anyone who asks My forgiveness that I may forgive him?”
Bukhari V8 book 75 no.:333
2/ An Hour On Friday.
a) The Prophet (Peace Be Upon Him) said:- “On Friday there is a particular time. If a Muslim happens to be praying and invoking Allah for something good during that time, Allah will surely fulfill his request.
The Prophet (Peace Be Upon Him) pointed out with his hand. We thought that he wanted to illustrate how short that time was” *
b) The Prophet (Peace Be Upon Him) said:- “Seek the time in which hope is placed on Friday from after the afternoon prayer till sunset” *
Bukhari V8 book 75, no:409 &Tirmidi Hadith 1360
3/ The Night Of Qadr (Decree)
This night in Ramadan is the greatest night of the year. The Almighty Allah said about it. “The night of Al-Qadar is better than a thousand months” Quran 97:3.
4/ The Dua Of A Muslim For is Muslim Brother Or Sister.
The Prophet (Peace Be Upon Him) said:- “He who supplicates for his brother behind his back (in his absence), the angel commissioned (for carrying dua to his Lord) says: ‘ Ameen, and it is for you also”.
Muslim book 035 no:6589.
5/ Dua During The Month Of Ramadan.
The Prophet (Peace Be Upon Him) said:- “When the month of Ramadan comes, the gates of mercy are opened and gates of Hell are locked and devils are chained”
Muslim book 6 no2361.
6./ A Traveller’s And Parent’s Dua.
The Prophet (Peace Be Upon Him) said: – three ( 3 ) duas are answered, there is no doubt about them:-
that of a father,
that of a traveler.
and that of one who has been wronged!
Abu Dawud book 8, # 1531.