Given that children can't exhibit the classical virtues in the same way that adults can, did Aristotle think that children could be happy? If so, in what sense?
Although Aristotle's eudaimonia is often loosely translated as "happiness" the meaning is quite different from the modern, subjective and emotional, idea. Aristotle's eudaimonia is objective and teleological, the human happiness is in fulfilling the function of a human being, which is, to Aristotle, living life guided by reason according to virtue. This is not as austere as it sounds, it involves acquiring, among other things, friends, wealth, and power. Be it as it may, this fulfilling is, by definition, a long-term process, not a sum total of instant, or even delayed, gratifications. Children, by their nature, can only be nurtured to get ready, they lack both developed reason or understanding of virtue to engage in it. This does not mean, of course, that they can not enjoy life, and draw pleasure from playing with friends, good food or reading books. Here is an accessible explanation of Aristotle's conception from Pursuit of Happiness, Aristotle:
"One of Aristotle's most influential works is the Nicomachean Ethics, where he presents a theory of happiness that is still relevant today, over 2,300 years later. The key question Aristotle seeks to answer in these lectures is "What is the ultimate purpose of human existence?" What is that end or goal for which we should direct all of our activities? Everywhere we see people seeking pleasure, wealth, and a good reputation. But while each of these has some value, none of them can occupy the place of the chief good for which humanity should aim. To be an ultimate end, an act must be self-sufficient and final, "that which is always desirable in itself and never for the sake of something else" (Nicomachean Ethics, 1097a30-34), and it must be attainable by man. Aristotle claims that nearly everyone would agree that happiness is the end which meets all these requirements...
The Greek word that usually gets translated as "happiness" is eudaimonia, and like most translations from ancient languages, this can be misleading. The main trouble is that happiness (especially in modern America) is often conceived of as a subjective state of mind, as when one says one is happy when one is enjoying a cool beer on a hot day, or is out "having fun" with one's friends. For Aristotle, however, happiness is a final end or goal that encompasses the totality of one's life. It is not something that can be gained or lost in a few hours, like pleasurable sensations. It is more like the ultimate value of your life as lived up to this moment, measuring how well you have lived up to your full potential as a human being. For this reason, one cannot really make any pronouncements about whether one has lived a happy life until it is over, just as we would not say of a football game that it was a "great game" at halftime (indeed we know of many such games that turn out to be blowouts or duds). For the same reason we cannot say that children are happy, any more than we can say that an acorn is a tree, for the potential for a flourishing human life has not yet been realized. As Aristotle says, "for as it is not one swallow or one fine day that makes a spring, so it is not one day or a short time that makes a man blessed and happy." (Nicomachean Ethics, 1098a18)".