Every sincerely asked Du'a will be accepted even if we don't see its results immediately. Allah knows the best and wants the best for us and He grants us whatever and whenever He knows the best for us.
Du'a needs sincerity, dedication, real faith in Allah and being away from sinful acts.
Best occasions for supplicating are many e.g. time of Azaan, between Azaan and Iqama, after every Salah, with and after Night prayer ( Namaz e Shabb), when rain falls, near the grave of parents and in the shrine of Imam Husain and other Imams of Ahlulbayt (AS).
It is always very good to supplicate during Sojood (Prostration) as the Hadeeth states the believers is nearest to Allah during prostration.
Wassalam.