Like Equanimity, all want Tranquility. Unfortunately, most want Tranquility for the wrong reason. People want Tranquility to compensate or to separate themselves from the lack of Tranquility which is manifested in Suffering and mental agitation.
The correct attitude is to see that Tranquility (Passaddhi-sambojjhanga) is the natural state of the human creature. There is no reason at all why the human should be experiencing stress, agitation or excitement.
HOW CAN ONE RECOGNIZE A TRANQUILITY THAT IS NOT EGOCENTRIC?
The Samyutta-nikāya Atthakatha explains that there are seven factors giving rise to Tranquility, thus eliminating the hindrances which dull the correct vision of Wisdom.
Now these do not mean that they develop Tranquility, but that in these seven conditions one can capture the cognitive experiences of Tranquility so as not to be deceived in other moments.
Experiencing a healthy and enjoyable meal without identity present.
Assuming a natural and comfortable posture of mind and body.
Exerting energy in a correct way without excess.
Being away from the presence of disturbed persons or civilization.
Associating with peaceful persons.
Directing oneself with Mindfulness.
Over a longer period of time, experiencing a comfortable season of the year which is peaceful or prosperous in which Identity has been absent.
TRANQUILITY DEVELOPED AT A PROFOUND LEVEL
Buddha stated in the Samyutta-nikāya:
"Monks, one must develop physical and mental tranquility through repeatedly practicing contemplations which are food for tranquility (Passaddhi-sambojjhanga), giving rise to tranquility which has not yet arisen and developing tranquility which has already arisen to become complete."
This is attained during Jhana meditations at the second level and is thus strengthened.
Most people tend to avoid these Jhana meditations, called Samatha, not realizing that the Vipassana which they adhere to, ignoring the Jhanas, is not an independent meditation. They are indeed two coupled meditative skills, Tranquility and Insight, which must in the most effective way possible be harnessed together:
In the Anguttara Nikaya it is stated:
"Some develop the Tranquility first and thereafter Insight and some develop Insight first and then Samatha. Both are correct. Others, indeed, can develop both in close harmony."
TRANQUILITY THROUGH ABIDING IN THE PRESENT MOMENT
Assuming now that you have the idea that Tranquility is not a situation to crave or to cling to, the question comes with regard to how it can be developed outside the Jhanas.
The only answer is by repeatedly practicing the Stillness of the mind whenever and as often as possible and developing a Mindfulness in Attention and in performing Tasks in Daily life.
You can see that this means dwelling in the present moment while letting go of the past and the future. This is not easy to do, and one of the best exercises is to simply sit quietly and dwell within the act of your own breathing. Breathing in, sensing the tactile experience at the nostrils, breathing out, sensing the tactile experience at the nostrils.
With this one-pointedness, Tranquility and freedom from thoughts is assured.