I have been through the same thing with my son, who is 13 and now pushing 5'8" and still growing. Two years ago, he was, maybe 5'. this time last year, he was maybe 5'3". He outgrew his 13" Trek 800 at the end of the summer of 2013. So, where will he wind up height wise? Based on my height (5'8", but used to be 5'9"), and the height of my wife's male relatives, he could be as tall as 6'2" or he could top out at 5'10" or 5'11". So, hard to say what size bike he would end up with. My estimate would be a 56 cm or 58 cm, or a M/L or even L. but right now he rides between a 53 and a 54 cm, or a M sized frame in some brands. I passed on a nice 52 Bianchi Volpe at a bike swap last month. My son was able to ride it, but I couldn't see paying money for a bike that was already on the small side for a growing boy, though it was a nice deal.

So my solution is to stick with what we have for another year. He has been riding my 90s era Bianchi hybrid, 18" frame, and should that get a little small, I might swap out for a longer stem as a stop gap. It isn't optimal, but he is more into mountain biking anyhow, and the hybrid is good enough for rides of up to 40 or 50 miles of road/bike trail riding, which he does maybe 3 or 4 times during the spring/summer season.

So, to sum up, I would recommend going with something used at the top of your boy's size range. If you can't find a road bike, maybe even consider a used hybrid with a solid fork. Those bikes can be found fairly cheap and might work as a stop gap until your boy's height stabilizes. In addition to being suitable for 30 or 40 mile rides or even longer, they are more versatile around town bikes than are true road bikes. And if your boy grows out of it, hopefully you can sell it for about what you paid for it and buy the next size up next year.