How can a Stern Gerlach apparatus be oriented in the $y$-plane? In the Stern-Gerlach experiment an image for the $z$ measurement is often shown (although the decision to call this orientation $z$ is arbitrary)
Stern-Gerlach in Z
It would seem that to make a measurement in the the $x$ direction that another apparatus would have to be placed and be turned $\pi/2$ around the axis of the beam.
However, the problem I've had with this line of reasoning is, what is this analogous to for the $y$ direction. Is the system rotated around an axis perpendicular to the beam?
It feels that this orientation would not deflect the particle. Some orientations may even have the particle not pass through the apparatus at all.
Question: Relative to the initial Stern-Gerlach, how is a $y$ orientation setup.
 A: "Relative to the initial Stern-Gerlach, how is a y orientation setup?"
The Stern-Gerlach uses a magnetic field gradient to spatially separate different spin-classes. The spatial separation occurs along the magnetic field gradient axis, as this gradient accelerates the atoms via their magnetic moment.
A "Stern-Gerlach experiment along the atomic beam axis" would work, but the spatial separation would occur along the beam axis, making it more difficult to detect. For example, you could place your strong magnetic field and field gradient along the beam propagation axis. This would accelerate a spin-class and de-accelerate the other along the beam propagation axis.
This means that if you shoot a small bunch of a few atoms, they would be separated temporally, ie. one spin-class would arrive at the detector slightly before than the other.
The detection difficulty comes from the fact that both spin-classes are still traveling along the same axis: if you were operating with a continuous source of atoms, you would only see one spot where both spin-classes are hitting the detector. But if you "chopped/pulsed" your source of atoms, you would see two spikes separated in time at the detector: each one corresponding to a different spin-class.
Somewhat off-topic note: you might want to check out a really cool apparatus called the "Zeeman slower".
