Which software to use to output molecular orbital diagrams?
If your interest is a qualitative reprepresentation, you may reach out for an editor like inkscape and use lines, squares and Unicode to create a picture like the following one

In text fields you may enter Ctrl + U followed by an unicode code like
2191 (for $\uparrow$), 2193 (for $\downarrow$), 21C5 (for $\uparrow\downarrow$).*) 
If you have access to LaTeX, you may be interested in modiagram, especially if you are interested in an output as .[e]ps or .pdf.  Only a few parameters are needed for an illustration like

(credit)
(It is possible to construct more advanced orbital diagrams like this and this, too.)

For the quantitative, and more programmatic approach you seek, especially with Python, there are solutions with the matplotlib library which might require some adaptation by you (example).  One of them is PyEnergyDiagrams once shown here on ChemSE:

the other EnergyLeveller.py:



Addition:  With the special chars used here, maybe a couple like Ipe + LaTeX is more handy to use, than inkscape.