You should have access to the AutoCAD Architectural Toolset, it does spiral stairs and rails. It took me only a few hours to figure out how to make a custom rail into a 4 board fence, so customization seems easy.
I just did a few simple spiral stairs, seems simple enough.
If needed in Autocad you'll need to Convert to 3D Solids.
Just get your engineering or surveying handbook out and look up horizontal curve you will find a diagram that has all the variables and how to work out the answers, just draw it and think about old school sin cos pythagoras etc.
This was like 1 minute on Google