Here they are:
1. The Last Third Of The Night
Abu Hurairah (RA) narrated that
Allah’s Messenger (SAW) said: 'In the
last third of every night our Rabb
(Cherisher and Sustainer) (Allah) descends to the lowermost heaven and says; "Who is calling Me,
so that I may answer him? Who is
asking Me so that may I grant him?
Who is seeking forgiveness from Me so that I may forgive him?."' [Sahih al-Bukhari, Hadith Qudsi] Amr ibn Absah narrated that the Prophet said: 'The closest any worshipper can be to His Lord is during the last part of the night, so if you can be amongst those who remember Allah at that time, then do so.'[at-Tirmidhi, an-Nasa'i, al-Hakim - Sahih]
2. Late at night
When people are sleeping and busy
with worldly pleasures Allah (SWT)
gives the believers an opportunity, or an answer hour if they can fight sleep and invoke Allah (SWT) for whatever they need. The Prophet (SAW) said:
'There is at night an hour, no Muslim
happens to be asking Allah any matter of this world or the Hereafter, except that he will be given it, and this (occurs) every night.' [Muslim #757]
3. Between Adhan and Iqamah
Anas (RA) narrated that Allah’s
Messenger (SAW) said: 'A supplication made between the Adhan and Iqama is not rejected.'
[Ahmad, abu Dawud #521, at-Tirmidhi #212, Sahih al-Jami #3408, an-Nasai and Ibn Hibban graded it sahih (sound)]
4. An Hour On Friday
Narrated Abu Hurairah (RA): Allah’s
Messenger (SAW) talked about Friday and said: 'There is an hour on Friday and if a Muslim gets it while offering Salat (prayer) and asks something from Allah (SWT), then Allah (SWT) will definitely meet his demand.' And he (the Prophet (SAW) pointed out the shortness of that particular time with his hands.[Sahih al-Bukhari]
Some have said that this hour is from the time the Imam (prayer’s leader) enters the mosque on Friday’s prayer until the prayer is over (ie between the two khutbahs), whereas others have said that it is the last hour of the day (ie after the Asr prayer until the Maghrib prayer).
5. While Drinking Zamzam Water Jaber (RA) narrated that Allah’s Messenger (SAW) said: 'Zamzam water is for what it is drunk for.' [Ahmad 3:357 and Ibn Majah #3062].
This means that when you drink Zamzam water you may ask Allah for
anything you like to gain or benefit
from this water such as healing from illness.... etc.
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 so it is best to invoke Allah 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.
7. 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, 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)
8. The Night Of 'Qadr' (Decree)
This night is the greatest night of the year. This is the night which the
almighty Allah said about it,
"The night of Al-Qadar (Decree) is
better than a thousand months." [Surah al-Qadr, 97: 3]
The Night of Decree is one of the odd nights of the last ten nights of the blessed month of Ramadan. The angels descend down to the earth, and the earth is overwhelmed with peace and serenity until the break of dawn and when he doors of Paradise are opened, the worshipper is encouraged to turn to Allah to ask for his needs for this world and the Hereafter.
9. During The Rain
Narrated Sahel Ibn Sa'ad (RA): that the Messenger of Allah (SAW) said: 'Two will not be rejected, Supplication when the Adhan (call of prayer) is being called, and at the time of the rain'. [Al- Hakim 2: 114, and Abu Dawud #2540, ibn Majah]
'Seek the response to your du'as when the armies meet, and the prayer is called, and when rain falls' [reported by Imam al-Shafi' in al-Umm, al-Sahihah #1469].
The time of the rain is a time of mercy from Allah so, one should take advantage of this time when Allah is having mercy on His slaves.
10. During Adhan
In another hadith; 'When the prayer is called, the doors of the skies are opened, and the du'a is answered' [al-Tayalisi in his Musnad #2106, al-Sahihah #1413]