According to Hadith, there are many times when dua is accepted, for example
after every obligatory salah, at the time of Tahajjud, between the time of Azan
and Iqamah, when it starts raining, while in a journey, doing dua after
praising Allah and reciting durood, doing dua in the sajdah of nafl salah. In
the sajdah, one should recite only the duas which are narrated from the Prophet
((صلى الله عليه وسلم, it is not allowed to do dua in sajdah in Urdu language.
The Prophet (صلى الله عليه وسلم) used to pray after every obligatory salah:
أللهم أنت السلام ومنك السلام
You should study in the books of Ahadiht the chapter: باب ما يقول بعد السلام,
you will find many traditions there. Also, there is a special chapter named
ابواب الدعوات containing a number of duas.
and Allah (Subhana Wa Ta'ala) Knows Best