Awesome question, I was trying to do that too and found a solution.
Using the dialog builder class AlertDialog.Builder you will have to invoke the dialog like this:
AlertDialog.Builder builder = new AlertDialog.Builder();
AlertDialog dialog;
builder.set...
dialog = builder.create();
dialog.getWindow().setSoftInputMode(LayoutParams.SOFT_INPUT_STATE_VISIBLE);
dialog.show();
This worked fine for me.
Note: you must import android.view.WindowManager.LayoutParams; for the constant value there.