bigjohn said:Of the two choices you present, the second - "on the morning of Sunday" - is the better choice, but still not very common. It sounds a bit stilted and overly formal for conversation and is more appropriate for writing. It is used to mark the importance or gravity of an event and would normally be followed by the actual date (e.g., "On the morning of Sunday, February 21..." - such and such happened).
If you alter the first one to "in the morning on Sunday" this would then be a well-formed option and appropriate for less formal occasions, but I would prefer just "on Sunday morning" for this purpose.
Please note that I am basing my judgments on usage in US English.