HCl rota-vibrational lab: ab initio simulation of rotation constants
Disclaimer:

I never used Gaussian, so I am just guessing about the program.

Coriolis coupling:

Coriolis coupling couples bending modes with rotation and there is no bending in diatomic molecules.

There is no Coriolis coupling in Gaussian for HCl, because there can't be one. The relevant output could also be NaN, it is simply not defined.

Alpha "matrix":

For diatomic molecules you have two degenerate rotations and one stretching mode. Hence your alpha "matrix" is actually well represented by a scalar and used as such in your equations. For this reason one would expect only one alpha value.

That there is written -0.000 and not 0.000 is an indication for a truncated negative number. In addition other values are properly set to NaN. I think that your one reported alpha value is simply close to zero. You can try a verbose output to verify this. 

Solution:

If you want to get a non zero alpha
I would recommend a molecule with a shallower potential hyper surface, i.e. a lower force constant. Or you could use this example to discuss floating point arithmetics and truncation with your students.