Exercise for meditation sitting

There are 2 types of exercises which you can apply here.

1. Physical
2. Mental

Physical

With regard to physical exercise is that you pratice sitting in a particular posture gradually increasing the duration of your sitting.

In meditation pratice by S.N.Goenka this is developed as part of developing your resolve as well as the ability to sit for a long hours.

Another p±ram² is adhiµµh±na—strong determination. When one starts a Vipassana course, one makes a determination to remain for the entire period of the course. One resolves to follow the precepts, the rule of silence, all the discipline of the course. After the introduction of the technique of Vipassana itself, one makes a strong determination to meditate for the entire hour during each group sitting without opening eyes, hands or legs. At a later stage on the path, this p±ram² will be very important; when coming close to the final goal, one must be ready to sit without break until reaching liberation. For this purpose it is necessary to develop strong determination.

Source: The Discourse Summaries by S.N.Goenka

Mental

In order to be able to sit for long hours you have to experience lightness in body and mind. You have to do this by actively releasing tensions by looking at gross solidified sensation part by part and if you have a free flow of subtle sensation in your body sweeping through them opens up the areas which are either numb or there is gross solidified sensations.

Also one way that the body will get lighter is to have sustained concentration on an object, i.e., you first bring your mind to the object (e.g. breath) then you continuously repeat the same metal redirection of the mind to the object regardless of the mind wandering away. Also walking meditation is able to develop stable concentration which intern will create lightness in the body.

For a more technical answer please see: Having trouble meditating long sessions (Physical pain)

Also I like to add the following note. Though in the 10 day meditation taught by S.N.Goenka there is no formal time allocated for walking meditation, walking is considered an antidote to drowsiness and sleepiness in the spirit of the following Sutta.

... Bhikshus, what more should be done? Bhikshus, you should train yourselves thus, We will devote ourselves to wakefulness. During the day, while walking to and fro and sitting down, we will purify the mind of obstructions. During the first watch of the night, while walking to and fro and sitting down, we will purify the mind of obstructions (avarana synonym for nīvarana). During the middle watch of the night, we will, after mentally noting the time for rising, mindfully and fully aware lie down, lion-like on our right side, one foot placed on the other. ...

Source: Maha Assa,pura Sutta. Also see footnote 30. The context here is staying awake and fighting drowsiness.

and

If, Moggallāna, that drowsiness still would not go away, then, Moggallāna, you should, perceiving before and after, be resolute in walking back and forth, with the senses turned inward, with the mind not straying outward. It is possible that when you do so, that drowsiness would go away.

Source: Pacalā Sutta. The context here is staying awake and fighting drowsiness.

These suttas only advocate this as an antidote to sleepiness and as a means to keep awake than any other form of pratice. This how S.N.Goenka teachers. This is inline with the Suttas.

Another enemy is laziness, drowsiness. All night you slept soundly, and yet when you sit to meditate, you feel very sleepy. This sleepiness is caused by your mental impurities, which would be driven out by the practice of Vipassana, and which therefore try to stop you from meditating. You must fight to prevent this enemy from overpowering you. Breathe slightly hard, or else get up, sprinkle cold water on your eyes, or walk a little, and then sit again.

Source: The Discourse Summaries

NB: Added this note as to there is no misunderstanding about this pratice, but not to condemn any other pratice.

Sorry for being something of a jerk , man. I just had one of those days :p

so to actually answer your question, it does depend on which tradition we're talking about.

I know some (all?) traditions within Tibetan Buddhism teach yoga/stretches, these kind of things.

Within the Theravada, stretching, yoga, exercise in general is not considered part of the practice, as far as formal meditation goes.

So from a Theravada perspective, I would submit to you that your best course of action would be to

1) Not solely sit for extended periods, much less an entire day. I've done this before at Goenka retreats, and I've found personally my meditation is much more productive when sitting is balanced with walking. I would also refer you to Ven. Yuttadhammo's answer to my question here

The Buddha did in fact teach just this practice:

Bhikkhus, you should train thus: ‘We will be devoted to wakefulness. During the day, while walking back and forth and sitting, we will purify our minds of obstructive states. In the first watch of the night, while walking back and forth and sitting, we will purify our minds of obstructive states. In the middle watch of the night we will lie down on the right side in the lion’s pose with one foot overlapping the other, mindful and fully aware, after noting in our minds the time for rising. After rising, in the third watch of the night, while walking back and forth and sitting, we will purify our minds of obstructive states.’

-- MN 39 (Bodhi, trans) This passage occurs frequently in the suttas. The Buddha taught there are five benefits to walking meditation:

addhānakkhamo hoti - one is able to tolerate long-distance travel

padhānakkhamo hoti - one is able to tolerate exertion

appābādho hoti - one has little sickness

asitaṃ pītaṃ khāyitaṃ sāyitaṃ sammā pariṇāmaṃ gacchati - what is eaten, drunk, chewed and tasted goes to proper digestion

caṅkamādhigato samādhi ciraṭṭhitiko hoti - walking-produced concentration is of long duration. -- AN 5.29

2) Meditate on the feeling of tired. Again, I'm not sure what personal practice you undertake, but within my practice it would be as simple as taking up the feeling as the object of meditation and noting "Tired, tired".

There's nothing really wrong with being tired, its just another transient state. The more you fight it, however, the more it will bite back :P You must bring about a clear awareness of it, look at how your mind reacts to it. It's nothing to go out of your way to stop arising, just like anything else. I hope this is actually of some use to you. Best of luck, be well.

The single best stretch you can do is the straddle stretch. The linked video is pretty fantastic in that it not only shows you the ideal, but also the progression leading up to it. Honorable mention goes to the frog pose. I also really like this sequence from Kelly Starrett. Ultimately, what you are going to want to pay attention to is hip mobility. Most meditators experience pain in the knees and back and tend to focus on stretches and exercises that target those two areas. Unbeknownst to them, what's really at issue is hip and psosas tightness. The pain they experience is a symptom of a problem farther up along the movement chain; it's being caused by the body trying to adapt to a less than ideal condition imposed by poor mobility elsewhere. Loosen up those other areas and the discomfort will lessen significantly.

And for the record, meditating for long periods of time should make you tired. That's kind of the point. ;-)