Stamina
The two minute trick should solve most physical stamina issues when playing the bagpipe. This section will deal with finger stamina exercises. This is particularly important when trying to make a step up from beginner to intemediate. Tunes do not get more difficult, only longer and more intense.
Mental stamina is also important. The practice method, when applied strictly, will result in a surprisingly high level of mental stamina; the main issues with this come as a result of situational management - that is managing performances.
Gracenote stamina
This pattern should be repeated using a single gracenote between each note. So for example, where we have GDE as the original form of this exercise, now you should play it using only High G gracenotes. When that is complete, only D gracenotes, then only E gracenotes, and then F gracenotes.
When all this has been achieved, then repeated the whole the whole lot again, with four gracenotes instead of three, and when that is done, use five...
The template is below:

An excess of exercises are not needed - do this well and it will do its job well!
Lip Stamina
This is perhaps one of the biggest single problems in piping - making your lips strong enough to last a whole tune.
There don't appear to be many answers to this, but the best candidate so far:
take the blowstick out of the pipes, put your finger half over the end which goes in the stock, and blow as hard as you can. Blow hard enough that fter a few breaths you get dizzy. Try to blow for as long as possible in single breaths - extend the length of each blow as much as you can and when your lips start to give way, keep going - it is in this moment that you will get the most results.
All and any suggestions regarding stamina are welcome!