Can the Greek word Teknon ever be used to mean young or dependent child as opposed to strictly son or daughter of any age?

Ioannis Manomenidis has tackled Modern Greek. Let me summarise:

• Téknon gets used by priests to their spiritual children, their congregation. There, it means neither offspring, nor child: it’s a metaphorical extension of the “child of God” or “child that I mentor” notion. But that’s an ancient Greek expression, limited to the ecclesiastical register.
• Evangelos Lolos delicately alluded to the mis-accented variant teknó. That means “toyboy”. It sounds like it comes from Kaliarda, the Greek gay cant (Καλιαρντά – Βικιπαίδεια). The thing is, you expect Romany vocabulary in Kaliarda, or “wrong” genders (Gender bender); but misaccentuation is not supposed to be part of Kaliarda’s repertoire.

  Well, as it turns out, teknó is Romany, from tiknó: Λεξικό της κοινής νεοελληνικής. It just sounded so similar to téknon, that the vowel was switched to match.

That was fun.

But I strongly suspect, OP, that you’re after the Ancient Greek meanings of téknon (when it was a current word), and likely you’re wanting some New Testament exegesis out of it.

Etymologically, téknon is derived from tíktō, “to give birth”. So it does originally mean son/daughter, not child.

Was it ever used for generic “child”? Let’s turn to Liddell-Scott, the canonical big dictionary of Ancient Greek, and BDAG, the New Testament dictionary. The other dictionaries don’t have the same kind of coverage, and are later anyway. (Trapp has only new words, and is late Byzantine; Lampe does Church Fathers, and spends more time on theology than generic semantics.)

LSJ. The definition is not that explicit, but in Odyssey 2.363, it is used to address Telemachus, not by his mother, but by his nurse Eurycleia. I’ve looked at several Attic instances, without finding a clear instance where it does not mean offspring. But LSJ itself treats παῖς “child” and τέκνον as interchangeable, and says that Attic tended to use παῖς instead.

Bauer asserts as definition 3 of téknon “one who is dear to another but without genetic relationship and without distinction in age”. That’s the “my spiritual child” meaning.