NOT true. Research suggests that coffee consumption has no effect on height. This Myth was started decades ago when it was thought that caffeine in coffee may be a risk for osteoporosis, and subsequently lead to reduced bone mass. However, much of the previous research that linked caffeine beverages and osteoporosis were made in populations that also had low calcium intakes. These people were most likely replacing calcium-rich milk with coffee or caffeine sodas. *Low calicum intakes are clearly linked to reduced bone health.
More recent studies suggest that even if caffeine does slightly offset calcium absorption, the effect is very small.... and it's easily offset by adding a couple of tablespoons of milk into your coffee. Of course, for optimal bone health you'll also need an appropriate daily dose of calcium throughout the day from low-fat dairy, fortified foods, certain greens and/or supplements.
So coffee won't stunt your kid's growth, should you still limit their consumption? Yes, because there are other potential adverse side effects including stomach discomfort, nervousness, shakiness, rapid heartbeat, insomnia, and irritability. In my opinion, it's NOT a good idea to let you child drink caffeinated coffee.