Cut the act.
Yes, offer her dad a firm handshake, and give her mother a compliment on her cooking, but make sure it all comes from a genuine place. If you have a plastic smile glued to your face for the entirety of the evening, and everything you say is stilted and blatantly appeasing them, you risk seeming insincere.
Instead, let them see what their daughter does. Sure, be somewhat reserved (i.e. politics, religion, money and sex should not enter the conversation), but also let them in a little bit. Tell a joke, rattle off a story or two, and let them get to know you. The more they feel like they're actually meeting a real person, rather than just another boyfriend trying win their favor, the more likely you are to, well, win their favor.