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?