Hi nissank
You must have misunderstood how to use Scotlandspeople. You can order any certificate through that site - it's provided by GRO Scotland, the same people Flattybasher suggests. I can order an extract of my birth record (1946) and those of my daughters and grandson on that site so you should have no problem. What you cannot do for that date is see the actual record online, but then you said you wanted an actual paper extract.
If you have problems then give us details of you dad's birth and we will check it out.
Imber