Hi,
Assuming that this is Oval leaved Privet we are talking about (the normal one), you can propagate it by taking strong cuttings of about 9 inches long. Cut just below the bottom node and trim the top above the top node. The cutting should be half the thickness of a pencil and usually the bottom of this year's growth. Take out a 'trench' 6 inches deep in a sheltered spot. Put an inch of sand in the base and insert your cuttings, firming in well with you hand. Leave until the spring and you should get some good root formation.