6. While Prostrating
Abu Hurairah (RA) narrated that Allah’s Messenger (SAW), said: 'The nearest a slave can be to his Lord is when he is prostrating, so invoke (supplicate) Allah (SWT) much in it. [Muslim, abu Dawud, an-Nasa'i and others, Sahih al-Jami #1175]
When a Muslim is in his Salat (prayer) he is facing Allah (SWT) and when he prostrates he is the nearest he can be to Allah (SWT) so it is best to invoke Allah (SWT) at this time. It is said that while in prostration, one should not ask for worldy needs (ie a nice car, a new job, etc), but for the Hereafter.
8. At The End Of The Obligatory Salat:
Narrated Abu Omamah (RA): that Allah’s Messenger (SAW) was asked, O Messenger of Allah, which supplication is heard (by Allah (SWT), he said the end of the night and at the end of the obligatory Salat (prayer) [at-Tirmidhi]. This time is after saying 'At-tahyat' , and before making Tasleem (finishing prayer)
15. Dua after praising Allah and giving salat on the Prophet (SAW) in the tashahhud at the end of salat.
Narrated Faddalah ibn Ubayd (RA): that the Messenger of Allah (SAW) said: 'When anyone of you makes du'a, let him start by glorifying his Lord and praising Him, then let him send blessings upon the Prophet (SAW), then let him pray for whatever he wants' [abu Dawud #1481, at-Tirmidhi #3477]