In my opinion, you can get an overly protective father to give you space by showing maturity and responsibility. The only reason he is protective is because he is concerned about you and therefore, don't give him a reason to be worried.
Ask him if his parents were this over-protective, and never gave him some "space". Sometimes as parents, we forget just how much of life is learned by experience. I also agree with Phantom, that you should demonstrate good judgement, and give him reason to trust you and your decisions. Once "burned", that is really hard to get back.