Constantine VII (908-959) commissioned the De Administrando Imperio (English translation available here as a PDF) for his son, the future Romanos II (959-963):

Hear now, my son, those things of which I think you should not be ignorant, and be wise that you may attain to government. For I maintain that while learning is a good thing for all the rest as well, who are subjects, yet it is especially so for you, who are bound to take thought for the safety of all, and to steer and guide the laden ship of the world.

It is far more of a handbook on how to be an emperor than Marcus Aurelius' Meditations, which is really a work of philosophy. The DAI is a very strange text, but in broad terms it contains anecdotes and tips for the heir to the empire regarding foreign policy. There are many accounts of various barbarian peoples' origins and recent history, as well as more tangible advice, which basically boils down to bribing the barbarians and fooling them with lies diplomatic niceties. One particular famous command is to never give important things like Greek fire, the imperial regalia and imperial brides to outsiders, unless of course you want to be struck down by fire from the heavens.

Constantine had also commissioned other important works like De Ceremoniis, a handbook detailing how court ceremonies should happen, and many other encyclopedic collections of classical learning. A set of particularly interesting military treatises were also commissioned, again as advice for his son, with regards to warfare. This kind of writing actually had a very long tradition in the Roman Empire, as both the emperor Maurice in the sixth century and Leo VI in the tenth century had written similar works to explain what strategies and tactics should be used in each situation (the Strategikon and the Taktika respectively).