(unusual move to answer my own question)

In fact this is duplicate:

* http://math.stackexchange.com/questions/914152/how-to-mark-rational-points-on-a-sphere

and the rational points are of course easy to find

$$ x=\frac{2u}{u^2+v^2+1};y=\frac{2v}{u^2+v^2+1};z=\frac{u^2+v^2-1}{u^2+v^2+1} $$ 

There is even a proof of equidistribution as a result of [Duke](http://www.math.ucla.edu/~wdduke/preprints/rational.pdf)  He shows that:

$$ \frac{\sum_{h(x)\leq T} \psi(x)}{\sum_{h(x)\leq T} \;\;1\;\;} \to \int_{S^2} \psi \, d\mu $$
for any function $\psi: S^2 \to \mathbb{C}$.  There is also general discussion of Bjorn Poonen in genral on [rational points on varieties](http://www-math.mit.edu/~poonen/papers/Qpoints.pdf)