Hmm... interesting question!
Best Destiny by Diane Carey has young Kirk (16 years old, IIRC). It's been so long since I read it, though, that I don't remember how good it is. (Sorry.)
Other than that, the only ones I recall are the three TOS
Starfleet Academy books, but note that they are YA books. The titles were:
Crisis on Vulcan by Brad & Barbara Strickland,
Aftershock by John Vornholt, and
Cadet Kirk by Diane Carey. (Thanks, MA!

) I've never read these ones, myself.
That's all I can think of myself at the moment, but I'm sure others will be along to mention the ones I've missed. Well,
The Final Reflection by John M. Ford has a young Spock in it (7 yo, IIRC), but it's more of a cameo in one scene. Great book, though!
EDIT: Ninja'd by
Therin!