As Chris says the fuelling berth opens in the mornings up until the arrival of the Scillonian III, call the harbourmaster up first as there may be a bit of a queue when the harbour is busy.
If that is not convenient for you, fuel can be obtained by can behind the buildings on the quay or at either of the other petrol stations which both have red diesel (one at Porthmellon industrial estate the other at the eastern end of Porthcressa).
Be prepared to pay a premium rate, it aint cheap.
If you need a lot you may have to pre-arrange. Long time ago but I was once involved in a Scillies refuel that needed more than was on the island at the time...