Ok, so I've made some progress, maybe someone can tell me if my solution makes sense or if I've gone down the wrong path.

As I see it there are a couple cases:

All Categorical Parents -> Categorical Child == Conditional Probability Table

All Continuous Parents -> Categorical Child == Softmax (or Bayes Point Machine)

All Categorical Parents -> Continuous Child == Conditional Gaussian Table (I'm assuming that all continous variables are Gaussians)

All Continuous Parents -> Continuous Child == Bayes Linear Regression

And the tricky ones:

Mixed Parents -> Categorical Child == Some sort of Conditional Softmax table?

Mixed Parents -> Continuous Child == Some sort of Conditional Linear Regression table?

Mixed Parents -> Categorical Child == Some sort of Conditional Softmax table?

Mixed Parents -> Categorical Child == Some sort of Conditional Softmax table?