This has got to be my Henry GOULDING. They all lived in the Ryde Area of Sydney. His son Henry James GOULDING had father's name as Henry James on NSW BMD website b/c and d/c. His daughter Lucy May had father as Henry on b/c and Henry James on d/c.
The next step is to see if Henry James GOULDING (sen.) is the Henry James GOULDING on the SAXON family website which I think is English.It gives Henry James a birth date of 1836 but no wife or offspring.