Center-align text with Python-pptx
from pptx.enum.text import PP_ALIGN
shape.paragraphs[0].alignment = PP_ALIGN.CENTER
This is taken directly from the Python pptx Docs. Does this not work for you? You said in your question that you've heard of PP_PARAGRAPH_ALIGNMENT
but can't get it working. What problems are arising?
You can view more information regarding Python pptx alignment here.
Scanny, who commented below me added a wonderful point that will solve your problem:
Paragraph alignment (also known as justification) is a property of a paragraph and must be applied individually to each paragraph. In the code you included in your question, if you add a line p.alignment = PP_ALIGN.CENTER
you should get what you're after.