If you're sure they're not going to blow on you (take some sick-sacs anyway), then set up staight & level at 1000-1500 agl or more, trimmed and at a low cruise power setting. have your passenger put something small like a set of car keys in the palm of their open hand. Then raise the nose smoothly to 15-20° above horizon. Then smoothly push over until you feel light in your belts and the keys rise off the passenger's hand.
Don't get carried away and get into negative g's. The engine will probably loose fuel supply and miss if it's carbureted. Also, the engine may loose oil pressure momentarily if not set up for inverted flight.
If you ease into it nice and smoothly, the zero g's are more fun than scarry. Rough or erratic flying will only scare people not accustomed to it. Tell the people onboard about the engine sputtering too. It may happen if you get caried away or hold negative too long.
Put some M&Ms or other candy on the front glareshield and have the passengers in the rear seat try to catch them in their mouth as you nose the plane over.
Be smooth and don't overstress the airframe. Watch out for excessive speed as well. I would recommend doing them at least 2500-3000 AGL so you can hang on to it a little longer, plus it gives you a little larger safety zone if ya know what I mean. Also, make sure that there aren't any lose articles in the airplane like chalks or oil that might interfere with flying the plane or hit someone on the head.
Actually i would do it exiting a climb. 1. your airspeed is well below VA hence no damage, and 2. you can ride out the 0 g longer. Even put it into a zoom climb and get the pitch att up about 20-30 degrees, then nose it over, that way you have 20-30 degrees more over the horizontal to play with. Carbed Cessnas will cause the float in the carb go up...results fuel starvation, but many turbines will get a low oil pressure warning. ..........dont ask!
In my instrustion days, I was the resident expert at this. Did it in everything from a C150 to a light twin. Here's what you do.
From cruise flight, enter a power off dive at about 10 degrees until you raise your airspeed almost to yellow line. Very smoothly pull back to a 10 to 15 degree climb (you'll get about 2 gs positive). Hold this until you get to 1.5 Vs. When you get there, smoothly push the nose back over to about 10 degrees nose down. You will get about 20 seconds of zero gs. This is how NASA's "Vomit Comit" does it (B707).
I would not recommend the M&M trick. Any loose object will fly backwards and lodge itself in the tail of the airplane. I once had an aft bulkhead pop off in a C150 and lost some stuff down the tail cone. I was lucky it didn't jam the flight controls.