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Actually there is a reference to this and it is this video where the Dalai Lama advises a group of people to meditate before going to bed and immediately after waking up.
Before after waking up: our mind is filled freshness,you are relaxed and generally this continues to the rest of the day! You can face your obstacles easier!
Before going to bed: The stress built up during the day has to be gradually released before you can fall asleep.You too help your body relax better!
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In Anapasati suttaLord budda tells,
There is the case where a monk, having gone to the wilderness, to the shade of a tree, or to an empty building, sits down folding his legs crosswise, holding his body erect, and setting mindfulness to the fore.1 Always mindful, he breathes in; mindful he breathes out.
Here we can take our room or meditating place while it's empty of sounds as the empty building,So in night and morning time is the best time for that because there is less noise in that time..Someone feels better in night before go to sleep and someone may feels better in morning if feels tired in night before sleep..So this can be applied for other meditations too,You can choose better time between before sleep and just after wake up
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Answering my own question after some research.
Immediately after we get up from sleep and just before we fall asleep the mind is in a different state of being than the usual day state.
So we can utilize this state of mind to do deeper into meditation and make huge progress.
The answer is do Samatha meditation with or without sitting. Try consciously and with lot of efforts not to have any thoughts at all. Try to be as aware as possible.
Stay aware and mindful.